初一的一元一次方程怎么解? 初一的一元一次方程怎么解啊？？？？？？？？？
\u521d\u4e00\u5e74\u7ea7\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u89e3\u7684\u65b9\u6cd5\u3002\u542b\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b
\u6559\u80b2\u91cd\u70b9\u548c\u96be\u70b9
\u91cd\u70b9\uff1a\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u548c\u89e3\u6cd5.
\u96be\u70b9\uff1a\u5b57\u6bcd\u7cfb\u6570\u7684\u6761\u4ef6\u7684\u8fd0\u7528\u548c\u516c\u5f0f\u53d8\u5f62.
\u6559\u5b66\u8fc7\u7a0b\u8bbe\u8ba1
\u4e00\u3001\u5bfc\u5165\u65b0\u8bfe
\u95ee\uff1a\u4ec0\u4e48\u53eb\u65b9\u7a0b?\u4ec0\u4e48\u53eb\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b?
\u7b54\uff1a\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f\u53eb\u505a\u65b9\u7a0b\uff0c\u542b\u6709\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u5e76\u4e14\u672a\u77e5\u6570\u7684\u6b21\u6570\u662f1\u7684\u65b9\u7a0b\u53eb\u505a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b.
\u4f8b \u89e3\u65b9\u7a0b2x\uff0d1 3\uff0d10x+1 6=2x+1 4\uff0d1
\u89e3 \u53bb\u5206\u6bcd\uff0c\u65b9\u7a0b\u4e24\u8fb9\u90fd\u4e58\u4ee512\uff0c\u5f97
4(2x\uff0d1)\uff0d2(10x+1)=3(2x+1)\uff0d12,
\u53bb\u62ec\u53f7\uff0c\u5f97
8x\uff0d4\uff0d20x\uff0d2=6x+3-12
\u79fb\u9879\uff0c\u5f97
8x\uff0d20x\uff0d6x=3-12+4+2\uff0c
\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u5f97
\uff0d18x=\uff0d3\uff0c
\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5\uff0d18\uff0c\u5f97
x=3 18 ,\u5373 x=1 6.
\u4e8c\u3001\u65b0\u8bfe
1.\u542b\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\u6cd5.
\u6211\u4eec\u628a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7528\u4e00\u822c\u7684\u5f62\u5f0f\u8868\u793a\u4e3a
ax=b (a\u22600),
\u5176\u4e2dx\u8868\u793a\u672a\u77e5\u6570\uff0ca\u548cb\u662f\u7528\u5b57\u6bcd\u8868\u793a\u7684\u5df2\u77e5\u6570\uff0c\u5bf9\u672a\u77e5\u6570x\u6765\u8bf4\uff0c\u5b57\u6bcda\u662fx\u7684\u7cfb\u6570\uff0c\u53eb\u505a\u5b57\u6bcd\u7cfb\u6570\uff0c\u5b57\u6bcdb\u662f\u5e38\u6570\u9879.
\u5982\u679c\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u4e2d\u7684\u7cfb\u6570\u7528\u5b57\u6bcd\u6765\u8868\u793a\uff0c\u90a3\u4e48\u8fd9\u4e2a\u65b9\u7a0b\u5c31\u53eb\u505a\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00
\u6b21\u65b9\u7a0b.
\u4ee5\u540e\u5982\u679c\u6ca1\u6709\u7279\u522b\u8bf4\u660e\uff0c\u5728\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\u4e2d\uff0c\u4e00\u822c\u7528a\uff0cb\uff0cc\u7b49\u8868\u793a\u5df2\u77e5\u6570\uff0c\u7528x\uff0cy\uff0cz\u7b49\u8868\u793a\u672a\u77e5\u6570.
\u542b\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\u6cd5\u4e0e\u53ea\u542b\u6709\u6570\u5b57\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\u6cd5\u76f8\u540c.\u6309\u7167\u89e3
\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u6b65\u9aa4\uff0c\u6700\u540e\u8f6c\u5316\u4e3aax=b(a\u22600)\u7684\u5f62\u5f0f.\u8fd9\u91cc\u5e94\u6ce8\u610f\u7684\u662f\uff0c\u7528\u542b\u6709\u5b57\u6bcd\u7684\u5f0f\u5b50\u53bb\u4e58\u6216\u9664\u65b9\u7a0b\u7684\u4e24\u8fb9\uff0c\u8fd9\u4e2a\u5f0f\u5b50\u7684\u503c\u4e0d\u80fd\u7b49\u4e8e\u96f6.\u5982(m\uff0d2)x=3,\u5fc5\u987b\u5f53m\uff0d2\u22600\u65f6\uff0c\u5373m\u22602\u65f6\uff0c\u624d\u6709x=3 m\uff0d2 .\u8fd9\u662f\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\u548c\u53ea\u542b\u6709\u6570\u5b57\u7cfb\u6570\u7684\u65b9\u7a0b\u7684\u91cd\u8981\u533a\u522b.
\u4f8b1 \u89e3\u65b9\u7a0bax+b2=bx+a2(a\u2260b).
\u5206\u6790\uff1a\u8fd9\u4e2a\u65b9\u7a0b\u4e2d\u7684\u5b57\u6bcda\uff0cb\u90fd\u662f\u5df2\u77e5\u6570\uff0cx\u662f\u672a\u77e5\u6570\uff0c\u662f\u4e00\u4e2a\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b.\u8fd9\u91cc\u7ed9\u51fa\u7684\u6761\u4ef6a\u2260b\uff0c\u662f\u4f7f\u65b9\u7a0b\u6709\u89e3\u7684\u5173\u952e\uff0c\u5728\u89e3\u65b9\u7a0b\u7684\u8fc7\u7a0b\u4e2d\u8981\u8fd0\u7528\u8fd9\u4e2a\u6761\u4ef6.
\u89e3 \u79fb\u9879\uff0c\u5f97
ax\uff0dbx=a2\uff0db2,
\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u5f97
(a\uff0db)x=a2\uff0db2.
\u56e0\u4e3aa\u2260b\uff0c\u6240\u4ee5a\uff0db\u22600.\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5a\uff0db\uff0c\u5f97
x=a2\uff0db2 a\uff0db=(a+b)(a\uff0db) a\uff0db,
\u6240\u4ee5 x=a+b.
\u6307\u51fa\uff1a
(1)\u9898\u4e2d\u7ed9\u51faa\u2260b\uff0c\u5728\u89e3\u65b9\u7a0b\u8fc7\u7a0b\u4e2d\uff0c\u4fdd\u8bc1\u4e86\u7528\u4e0d\u7b49\u4e8e\u96f6\u7684\u5f0f\u5b50a\uff0db\u53bb\u9664\u65b9\u7a0b\u7684\u4e24\u8fb9\u540e\u6240\u5f97\u7684\u65b9\u7a0b\u7684\u89e3\u662f\u539f\u65b9\u7a0b\u7684\u89e3\uff1b
(2)\u5982\u679c\u65b9\u7a0b\u7684\u89e3\u662f\u5206\u5f0f\u5f62\u5f0f\u65f6\uff0c\u4e00\u822c\u8981\u5316\u6210\u6700\u7b80\u5206\u5f0f\u6216\u6574\u5f0f.
\u4f8b2 x\uff0db a=2\uff0dx\uff0da b(a+b\u22600).
\u89c2\u5bdf\u65b9\u7a0b\u7ed3\u6784\u7684\u7279\u70b9\uff0c\u8bf7\u8bf4\u51fa\u89e3\u65b9\u7a0b\u7684\u601d\u8def.
\u7b54\uff1a\u8fd9\u4e2a\u65b9\u7a0b\u4e2d\u542b\u6709\u5206\u5f0f\uff0c\u53ef\u5148\u53bb\u5206\u6bcd\uff0c\u628a\u65b9\u7a0b\u8f6c\u5316\u6210\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b
\u7684\u4e00\u822c\u5f62\u5f0f.\u5728\u65b9\u7a0b\u53d8\u5f62\u4e2d\uff0c\u8981\u5e94\u7528\u5df2\u77e5\u6761\u4ef6a+b\u22600.
\u89e3 \u53bb\u5206\u6bcd\uff0c\u65b9\u7a0b\u4e24\u8fb9\u90fd\u4e58\u4ee5ab\u5f97
b(x\uff0db)=2ab\uff0da(x\uff0da),
\u53bb\u62ec\u53f7\uff0c\u5f97
bx\uff0db2=2ab\uff0dax+a2,
\u79fb\u9879\uff0c\u5f97
ax+bx=a2+2ab+b2
\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u5f97
(a+b)x=(a+b)2.
\u56e0\u4e3aa+b\u22600\uff0c\u6240\u4ee5x=a+b.
\u6307\u51fa\uff1aab\u22600\u662f\u4e00\u4e2a\u9690\u542b\u6761\u4ef6\uff0c\u8fd9\u662f\u56e0\u4e3a\u5b57\u6bcda\uff0cb\u5206\u522b\u662f\u65b9\u7a0b\u4e2d\u7684\u4e24\u4e2a\u5206\u5f0f\u7684\u5206\u6bcd\uff0c\u56e0\u6b64a\u22600,b\u22600,\u6240\u4ee5ab\u22600.
\u4f8b3 \u89e3\u5173\u4e8ex\u7684\u65b9\u7a0b
a2+(x\uff0d1)ax+3a=6x+2(a\u22602,a\u2260\uff0d3).
\u89e3 \u628a\u65b9\u7a0b\u53d8\u5f62\u4e3a\uff0c\u5f97
a2x\uff0da2+ax+3a=6x+2,
\u79fb\u9879\uff0c\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u5f97
a2x+ax\uff0d6x=a2\uff0d3a+2,
(a2+a\uff0d6)x=a2\uff0d3a+2,
(a+3)(a\uff0d2)x=(a\uff0d1)(a\uff0d2).
\u56e0\u4e3aa\u22602,a=\uff0d3\uff0c\u6240\u4ee5a+3\u22600\uff0ca\uff0d2\u22600.\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5(a+3)(a\uff0d2)\uff0c\u5f97
x=a\uff0d1 a+3.
2.\u516c\u5f0f\u53d8\u5f62.
\u5728\u7269\u7406\u8bfe\u4e2d\u6211\u4eec\u5b66\u4e60\u4e86\u5f88\u591a\u7269\u7406\u516c\u5f0f\uff0c\u5982\u679cq\u8868\u793a\u71c3\u70e7\u503c\uff0cm\u8868\u793a\u71c3\u6599\u7684\u8d28\u91cf\uff0c\u90a3\u4e48\u5b8c\u5168\u71c3\u70e7\u8fd9\u4e9b\u71c3\u6599\u4ea7\u751f\u7684\u70ed\u91cfW\uff0c\u4e09\u8005\u4e4b\u95f4\u7684\u5173\u7cfb\u4e3aW=qm\uff0c\u53c8\u5982\uff0c\u7528Q\u8868\u793a\u901a\u8fc7\u5f02\u4f53\u6a2a\u622a\u9762\u7684\u7535\u91cf\uff0c\u7528t\u8868\u793a\u65f6\u95f4\uff0c\u7528I\u8868\u793a\u901a\u8fc7\u5bfc\u4f53\u7535\u6d41\u7684\u5927\u5c0f\uff0c\u4e09\u8005\u4e4b\u95f4\u7684\u5173\u7cfb\u4e3aI=Qt.\u5728\u8fd9\u4e2a\u516c\u5f0f\u4e2d\uff0c\u5982\u679c\u7528I\u548ct\u6765\u8868\u793aQ\uff0c\u4e5f\u5c31\u662f\u5df2\u77e5I\u548ct\uff0c\u6c42Q\uff0c\u5c31\u5f97\u5230Q=It\uff1b\u5982\u679c\u7528I\u548cQ\u6765\u8868\u793at\uff0c\u4e5f\u5c31\u662f\u5df2\u77e5I\u548cQ\uff0c\uff0c\u6c42t\uff0c\u5c31\u5f97\u5230t=QI.
\u50cf\u4e0a\u9762\u8fd9\u6837\uff0c\u628a\u4e00\u4e2a\u516c\u5f0f\u4ece\u4e00\u79cd\u5f62\u5f0f\u53d8\u6362\u6210\u53e6\u4e00\u79cd\u5f62\u5f0f\uff0c\u53eb\u505a\u516c\u5f0f\u53d8\u5f62.
\u628a\u516c\u5f0f\u4e2d\u7684\u67d0\u4e00\u4e2a\u5b57\u6bcd\u4f5c\u4e3a\u672a\u77e5\u91cf\uff0c\u5176\u5b83\u7684\u5b57\u6bcd\u4f5c\u4e3a\u5df2\u77e5\u91cf\uff0c\u6c42\u672a\u77e5\u91cf\uff0c\u5c31\u662f\u89e3\u542b\u5b57\u6bcd
\u7cfb\u6570\u6570\u7684\u65b9\u7a0b.\u4e5f\u5c31\u662f\u8bf4\uff0c\u516c\u5f0f\u53d8\u5f62\u5b9e\u9645\u5c31\u662f\u89e3\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b.\u516c\u5f0f\u53d8\u5f62\u4e0d\u4f46\u5728\u6570\u5b66\uff0c\u800c\u4e14\u5728\u7269\u7406\u548c\u5316\u5b66\u7b49\u5b66\u79d1\u4e2d\u975e\u5e38\u91cd\u8981\uff0c\u6211\u4eec\u8981\u719f\u7ec3\u638c\u63e1\u516c\u5f0f\u53d8\u5f62\u7684\u6280\u80fd.
\u4f8b4 \u5728\u516c\u5f0f\u03c5=\u03c5o+at\u4e2d\uff0c\u5df2\u77e5\u03c5,\u03c5o,a\uff0c\u4e14a\u22600\uff0c\u6c42t.
\u5206\u6790\uff1a\u5df2\u77e5\u03c5\uff0c\u03c5o\u548ca\uff0c\u6c42t\uff0c\u4e5f\u5c31\u662f\u628a\u03c5\uff0c\u03c5o\u548ca\u4f5c\u4e3a\u5df2\u77e5\u91cf\uff0c\u89e3\u5173\u4e8e\u672a\u77e5\u91cft\u7684\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b.
\u89e3 \u79fb\u9879\uff0c\u5f97
\u03c5\uff0d\u03c50=at.
\u56e0\u4e3aa\u22600\uff0c\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5a,\u5f97
t=\u03c5\uff0d\u03c5o a.
\u4f8b5 \u5728\u68af\u5f62\u9762\u79ef\u516c\u5f0fs=12(a+b)h\u4e2d\uff0c\u5df2\u77e5a\uff0cb\uff0ch\u4e3a\u6b63\u6570.
(1)\u7528s\uff0ca\uff0cb\u8868\u793ah\uff1b(2)\u7528S,b,h\u8868\u793aa.
\u95ee\uff1a(1)\u548c(2)\u4e2d\u54ea\u4e9b\u662f\u5df2\u77e5\u91cf?\u54ea\u4e9b\u662f\u672a\u77e5\u91cf\uff1b
\u7b54\uff1a\uff081\uff09\u4e2dS\uff0ca\uff0cb\u662f\u5df2\u77e5\u91cf\uff0ch\u662f\u672a\u77e5\u91cf;(2)\u4e2ds\uff0cb\uff0ch\u90fd\u662f\u77e5\u5df2\u91cf\uff0ca\u662f\u672a\u77e5\u91cf.
\u89e3 (1)\u65b9\u7a0b\u4e24\u8fb9\u90fd\u4e58\u4ee52\uff0c\u5f97
2s=(a+b)h.
\u56e0\u4e3aa\u4e0eb\u90fd\u662f\u6b63\u6570\uff0c\u6240\u4ee5a\u22600\uff0cb\u22600\uff0c\u5373a+b\u22600\uff0c\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5a+b\uff0c\u5f97
h=2sa+b.
(2)\u65b9\u7a0b\u4e24\u8fb9\u90fd\u4e58\u4ee52\uff0c\u5f97
2s=(a+b)h,
\u6574\u7406\uff0c\u5f97
ah=2s\uff0dbh.
\u56e0\u4e3ah\u4e3a\u6b63\u6570\uff0c\u6240\u4ee5h\u22600\uff0c\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5h,\u5f97
a=2s\uff0dbh h.
\u6307\u51fa\uff1a\u9898\u662f\u89e3\u5173\u4e8eh\u7684\u65b9\u7a0b\uff0c(a+b)\u53ef\u770b\u4f5c\u662f\u672a\u77e5\u91cfh\u7684\u7cfb\u6570\uff0c\u5728\u8fd0\u7b97\u4e2d(a+b)h\u4e0d\u8981\u5c55\u5f00.
\u4e09\u3001\u8bfe\u5802\u7ec3\u4e60
1.\u89e3\u4e0b\u5217\u5173\u4e8ex\u7684\u65b9\u7a0b\uff1a
(1)3a+4x=7x\uff0d5b; (2)xa\uff0db=xb\uff0da(a\u2260b)\uff1b
(3)m2(x\uff0dn)=n2(x\uff0dm)(m2\u2260n2);
(4)ab+xa=xb\uff0dba(a\u2260b);
(5)a2x+2=a(x+2)(a\u22600,a\u22601).
2.\u586b\u7a7a\uff1a
(1)\u5df2\u77e5y=rx+b r\u22600,\u5219x=_______;
(2)\u5df2\u77e5F=ma,a\u22600\uff0c\u5219m=_________;
(3)\u5df2\u77e5ax+by=c\uff0ca\u22600\uff0c\u5219x=_______.
3.\u4ee5\u4e0b\u516c\u5f0f\u4e2d\u7684\u5b57\u6bcd\u90fd\u4e0d\u7b49\u4e8e\u96f6.
(1)\u6c42\u51fa\u516c\u5f0fm=pn+2\u4e2d\u7684n;
(2)\u5df2\u77e5xa+1b=1m\uff0c\u6c42x\uff1b
(3)\u5728\u516c\u5f0fS=a+b2h\u4e2d\uff0c\u6c42a;
(4)\u5728\u516c\u5f0fS=\u03c5ot+12t2x\u4e2d\uff0c\u6c42x.
\u7b54\u6848\uff1a
1.(1)x=3a+5b 3\uff1b (2)x=ab; (3)x=mn m+n; (4)x=a2+b2 a\uff0db (5)x=2a.
2.(1)x=y\uff0db r\uff1b (2)m=Fa; (3)x=c\uff0dby a.
3.(1)n=p\uff0d2m m; (2)x=ab\uff0dam bm; (3)a=2s\uff0dbh h;
(4)x=2s\uff0d2\u03c5ott2.
\u56db\u3001\u5c0f\u7ed3
1.\u542b\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u4e0e\u53ea\u542b\u6709\u6570\u5b57\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\u6cd5\u76f8\u540c\uff0c\u4f46\u5e94\u7279\u522b\u6ce8\u610f\uff0c\u7528\u542b\u6709\u5b57\u6bcd\u7684\u5f0f\u5b50\u53bb\u4e58\u6216\u9664\u65b9\u7a0b\u7684\u4e24\u8fb9\u65f6\uff0c\u8fd9\u4e2a\u5f0f\u5b50\u7684\u503c\u4e0d\u80fd\u4e3a\u96f6.\u6211\u4eec\u6240\u4e3e\u7684\u4f8b\u9898\u53ca\u8bfe\u5802\u7ec3\u4e60\u7684\u9898\u76ee\u4e2d\u6240\u7ed9\u51fa\u7684\u6761\u4ef6\uff0c\u90fd\u4fdd\u8bc1\u4e86\u8fd9\u4e00\u70b9.
2.\u5bf9\u4e8e\u516c\u5f0f\u53d8\u5f62\uff0c\u9996\u5148\u8981\u5f04\u6e05\u516c\u5f0f\u4e2d\u54ea\u4e9b\u662f\u5df2\u77e5\u91cf\uff0c\u54ea\u4e2a\u662f\u672a\u77e5\u91cf.\u628a\u5df2\u77e5\u91cf\u4f5c\u4e3a\u5b57
\u6bcd\u7cfb\u6570\uff0c\u6c42\u672a\u77e5\u91cf\u7684\u8fc7\u7a0b\u5c31\u662f\u89e3\u5173\u4e8e\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\u7684\u8fc7\u7a0b.
\u4e94\u3001\u4f5c\u4e1a
1\uff0e\u89e3\u4e0b\u5217\u5173\u4e8ex\u7684\u65b9\u7a0b
(1)(m2+n2)x=m2\uff0dn2+2mnx(m\uff0dn\u22600)\uff1b
(2)(x\uff0da)2\uff0d(x\uff0db)2=2a2\uff0d2b2 (a\uff0db\u22600);
(3)x+xm=m(m\u2260\uff0d1);
(4)xb+b=xa+a(a\u2260b);
(5)m+nx m+n=a+bx a+b(mb\u2260na).
2.\u5728\u516c\u5f0fM=D\uff0dd 2l\u4e2d\uff0c\u6240\u6709\u7684\u5b57\u6bcd\u90fd\u4e0d\u7b49\u4e8e\u96f6.
(1)\u5df2\u77e5M,l ,d\u6c42D\uff1b (2)\u5df2\u77e5M,l D,\u6c42d.
3.\u5728\u516c\u5f0fS=12n[a1+(n\uff0d1)d]\u4e2d\uff0c\u6240\u6709\u7684\u5b57\u6bcd\u90fd\u662f\u6b63\u6570\uff0c\u800c\u4e14n\u4e3a\u5927\u4e8e1\u7684\u6574\u6570\uff0c\u6c42d.
\u7b54\u6848\uff1a
1.(1)x=m+n m\uff0dn; (2)x=\uff0da+b 2; (3)x=m2 m+1; (4)x=ab; (5)x=1.
2.(1)D=2lM+d; (2)d=D\uff0d2lM.
3.d=2S\uff0dna1 n(n\uff0d1).
\u8bfe\u5802\u6570\u5b66\u8bbe\u8ba1\u8bf4\u660e
1.\u5b66\u751f\u5bf9\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\u7684\u8ba4\u8bc6\u548c\u89e3\u6cd5\u4ee5\u53ca\u516c\u5f0f\u53d8\u5f62\uff0c\u63a5\u53d7\u8d77\u6765\u6709\u4e00\u5b9a\u56f0\u96be.\u542b\u5b57
\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\u4e0e\u53ea\u542b\u6570\u5b57\u7cfb\u6570\u7684\u65b9\u7a0b\u7684\u5173\u7cfb\uff0c\u662f\u4e00\u822c\u4e0e\u7279\u6b8a\u7684\u5173\u7cfb\uff0c\u5f53\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b
\u4e2d\u7684\u5b57\u6bcd\u7ed9\u51fa\u7279\u5b9a\u7684\u6570\u5b57\u65f6\uff0c\u5c31\u662f\u53ea\u542b\u6570\u5b57\u7cfb\u6570\u7684\u65b9\u7a0b.\u6240\u4ee5\u5728\u6559\u5b66\u8bbe\u8ba1\u4e2d\u662f\u4ece\u590d\u4e60\u89e3\u53ea\u542b
\u6570\u5b57\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u5165\u624b\uff0c\u8fc7\u6e21\u5230\u8ba8\u8bba\u542b\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\u6cd5\u548c\u516c\u5f0f\u53d8\u5f62\uff0c
\u4f53\u73b0\u4e86\u9075\u5faa\u5b66\u751f\u4ece\u5177\u4f53\u5230\u62bd\u8c61\uff0c\u4ece\u7279\u6b8a\u5230\u4e00\u822c\u7684\u601d\u7ef4\u65b9\u5f0f\u548c\u8ba4\u8bc6\u4e8b\u7269\u7684\u89c4\u5f8b.
2.\u5728\u4ee3\u6570\u6559\u5b66\u4e2d\u5e94\u6ce8\u610f\u6e17\u900f\u63a8\u7406\u56e0\u7d20.\u5728\u89e3\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u548c\u516c\u5f0f\u53d8\u5f62\u7684\u8fc7\u7a0b\u4e2d\uff0c\u5f15\u5bfc\u5b66\u751f\u6ce8\u610f\u6240\u7ed9\u9898\u4e2d\u7684\u5df2\u77e5\u6761\u4ef6\u662f\u4ec0\u4e48\uff0c\u5728\u65b9\u7a0b\u53d8\u5f62\u4e2d\u8981\u6b63\u786e\u8fd0\u7528\u9898\u4e2d\u7684\u5df2\u77e5\u6761\u4ef6.\u5982\u5728\u89e3\u65b9\u7a0b\u4e2d\uff0c\u5e38\u7528\u542b\u6709\u5b57\u6bcd\u7684\u5f0f\u5b50\u4e58(\u6216\u9664)\u65b9\u7a0b\u7684\u4e24\u8fb9\uff0c\u5e76\u8981\u8bba\u8ff0\u5982\u4f55\u6839\u636e\u5df2\u77e5\u6761\u4ef6\uff0c\u4fdd\u8bc1\u8fd9\u4e2a\u5f0f\u5b50\u7684\u503c\u4e0d\u7b49\u4e8e\u96f6\uff0c\u4ece\u4e2d\u6709\u610f\u8bc6\u5730\u8bad\u7ec3\u548c\u63d0\u9ad8\u5b66\u751f\u7684\u903b\u8f91\u63a8\u7406\u80fd\u529b\uff0c\u628a\u4ee3\u6570\u8fd0\u7b97\u548c\u63a8\u7406\u871c\u5207\u7ed3\u5408.
\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f\u53eb\u505a\u65b9\u7a0b\uff0c\u542b\u6709\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u5e76\u4e14\u672a\u77e5\u6570\u7684\u6b21\u6570\u662f1\u7684\u65b9\u7a0b\u53eb\u505a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b.
\u4f8b \u89e3\u65b9\u7a0b2x\uff0d1 3\uff0d10x+1 6=2x+1 4\uff0d1
\u89e3 \u53bb\u5206\u6bcd\uff0c\u65b9\u7a0b\u4e24\u8fb9\u90fd\u4e58\u4ee512\uff0c\u5f97
4(2x\uff0d1)\uff0d2(10x+1)=3(2x+1)\uff0d12,
\u53bb\u62ec\u53f7\uff0c\u5f97
8x\uff0d4\uff0d20x\uff0d2=6x+3-12
\u79fb\u9879\uff0c\u5f97
8x\uff0d20x\uff0d6x=3-12+4+2\uff0c
\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u5f97
\uff0d18x=\uff0d3\uff0c
\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5\uff0d18\uff0c\u5f97
x=3 18 ,\u5373 x=1 6. \u6211\u4eec\u628a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7528\u4e00\u822c\u7684\u5f62\u5f0f\u8868\u793a\u4e3a
ax=b (a\u22600),
\u5176\u4e2dx\u8868\u793a\u672a\u77e5\u6570\uff0ca\u548cb\u662f\u7528\u5b57\u6bcd\u8868\u793a\u7684\u5df2\u77e5\u6570\uff0c\u5bf9\u672a\u77e5\u6570x\u6765\u8bf4\uff0c\u5b57\u6bcda\u662fx\u7684\u7cfb\u6570\uff0c\u53eb\u505a\u5b57\u6bcd\u7cfb\u6570\uff0c\u5b57\u6bcdb\u662f\u5e38\u6570\u9879.
\u5982\u679c\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u4e2d\u7684\u7cfb\u6570\u7528\u5b57\u6bcd\u6765\u8868\u793a\uff0c\u90a3\u4e48\u8fd9\u4e2a\u65b9\u7a0b\u5c31\u53eb\u505a\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00
\u6b21\u65b9\u7a0b.
\u4ee5\u540e\u5982\u679c\u6ca1\u6709\u7279\u522b\u8bf4\u660e\uff0c\u5728\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\u4e2d\uff0c\u4e00\u822c\u7528a\uff0cb\uff0cc\u7b49\u8868\u793a\u5df2\u77e5\u6570\uff0c\u7528x\uff0cy\uff0cz\u7b49\u8868\u793a\u672a\u77e5\u6570.
\u542b\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\u6cd5\u4e0e\u53ea\u542b\u6709\u6570\u5b57\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\u6cd5\u76f8\u540c.\u6309\u7167\u89e3
\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u6b65\u9aa4\uff0c\u6700\u540e\u8f6c\u5316\u4e3aax=b(a\u22600)\u7684\u5f62\u5f0f.\u8fd9\u91cc\u5e94\u6ce8\u610f\u7684\u662f\uff0c\u7528\u542b\u6709\u5b57\u6bcd\u7684\u5f0f\u5b50\u53bb\u4e58\u6216\u9664\u65b9\u7a0b\u7684\u4e24\u8fb9\uff0c\u8fd9\u4e2a\u5f0f\u5b50\u7684\u503c\u4e0d\u80fd\u7b49\u4e8e\u96f6.\u5982(m\uff0d2)x=3,\u5fc5\u987b\u5f53m\uff0d2\u22600\u65f6\uff0c\u5373m\u22602\u65f6\uff0c\u624d\u6709x=3 m\uff0d2 .\u8fd9\u662f\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\u548c\u53ea\u542b\u6709\u6570\u5b57\u7cfb\u6570\u7684\u65b9\u7a0b\u7684\u91cd\u8981\u533a\u522b.
\u4f8b1 \u89e3\u65b9\u7a0bax+b2=bx+a2(a\u2260b).
\u5206\u6790\uff1a\u8fd9\u4e2a\u65b9\u7a0b\u4e2d\u7684\u5b57\u6bcda\uff0cb\u90fd\u662f\u5df2\u77e5\u6570\uff0cx\u662f\u672a\u77e5\u6570\uff0c\u662f\u4e00\u4e2a\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b.\u8fd9\u91cc\u7ed9\u51fa\u7684\u6761\u4ef6a\u2260b\uff0c\u662f\u4f7f\u65b9\u7a0b\u6709\u89e3\u7684\u5173\u952e\uff0c\u5728\u89e3\u65b9\u7a0b\u7684\u8fc7\u7a0b\u4e2d\u8981\u8fd0\u7528\u8fd9\u4e2a\u6761\u4ef6.
\u89e3 \u79fb\u9879\uff0c\u5f97
ax\uff0dbx=a2\uff0db2,
\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u5f97
(a\uff0db)x=a2\uff0db2.
\u56e0\u4e3aa\u2260b\uff0c\u6240\u4ee5a\uff0db\u22600.\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5a\uff0db\uff0c\u5f97
x=a2\uff0db2 a\uff0db=(a+b)(a\uff0db) a\uff0db,
\u6240\u4ee5 x=a+b.
\u6307\u51fa\uff1a
(1)\u9898\u4e2d\u7ed9\u51faa\u2260b\uff0c\u5728\u89e3\u65b9\u7a0b\u8fc7\u7a0b\u4e2d\uff0c\u4fdd\u8bc1\u4e86\u7528\u4e0d\u7b49\u4e8e\u96f6\u7684\u5f0f\u5b50a\uff0db\u53bb\u9664\u65b9\u7a0b\u7684\u4e24\u8fb9\u540e\u6240\u5f97\u7684\u65b9\u7a0b\u7684\u89e3\u662f\u539f\u65b9\u7a0b\u7684\u89e3\uff1b
(2)\u5982\u679c\u65b9\u7a0b\u7684\u89e3\u662f\u5206\u5f0f\u5f62\u5f0f\u65f6\uff0c\u4e00\u822c\u8981\u5316\u6210\u6700\u7b80\u5206\u5f0f\u6216\u6574\u5f0f.
\u4f8b2 x\uff0db a=2\uff0dx\uff0da b(a+b\u22600).
\u89c2\u5bdf\u65b9\u7a0b\u7ed3\u6784\u7684\u7279\u70b9\uff0c\u8bf7\u8bf4\u51fa\u89e3\u65b9\u7a0b\u7684\u601d\u8def.
\u7b54\uff1a\u8fd9\u4e2a\u65b9\u7a0b\u4e2d\u542b\u6709\u5206\u5f0f\uff0c\u53ef\u5148\u53bb\u5206\u6bcd\uff0c\u628a\u65b9\u7a0b\u8f6c\u5316\u6210\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b
\u7684\u4e00\u822c\u5f62\u5f0f.\u5728\u65b9\u7a0b\u53d8\u5f62\u4e2d\uff0c\u8981\u5e94\u7528\u5df2\u77e5\u6761\u4ef6a+b\u22600.
\u89e3 \u53bb\u5206\u6bcd\uff0c\u65b9\u7a0b\u4e24\u8fb9\u90fd\u4e58\u4ee5ab\u5f97
b(x\uff0db)=2ab\uff0da(x\uff0da),
\u53bb\u62ec\u53f7\uff0c\u5f97
bx\uff0db2=2ab\uff0dax+a2,
\u79fb\u9879\uff0c\u5f97
ax+bx=a2+2ab+b2
\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u5f97
(a+b)x=(a+b)2.
\u56e0\u4e3aa+b\u22600\uff0c\u6240\u4ee5x=a+b.
\u6307\u51fa\uff1aab\u22600\u662f\u4e00\u4e2a\u9690\u542b\u6761\u4ef6\uff0c\u8fd9\u662f\u56e0\u4e3a\u5b57\u6bcda\uff0cb\u5206\u522b\u662f\u65b9\u7a0b\u4e2d\u7684\u4e24\u4e2a\u5206\u5f0f\u7684\u5206\u6bcd\uff0c\u56e0\u6b64a\u22600,b\u22600,\u6240\u4ee5ab\u22600.
\u4f8b3 \u89e3\u5173\u4e8ex\u7684\u65b9\u7a0b
a2+(x\uff0d1)ax+3a=6x+2(a\u22602,a\u2260\uff0d3).
\u89e3 \u628a\u65b9\u7a0b\u53d8\u5f62\u4e3a\uff0c\u5f97
a2x\uff0da2+ax+3a=6x+2,
\u79fb\u9879\uff0c\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u5f97
a2x+ax\uff0d6x=a2\uff0d3a+2,
(a2+a\uff0d6)x=a2\uff0d3a+2,
(a+3)(a\uff0d2)x=(a\uff0d1)(a\uff0d2).
\u56e0\u4e3aa\u22602,a=\uff0d3\uff0c\u6240\u4ee5a+3\u22600\uff0ca\uff0d2\u22600.\u65b9\u7a0b\u4e24\u8fb9\u90fd\u9664\u4ee5(a+3)(a\uff0d2)\uff0c\u5f97
x=a\uff0d1 a+3.
第一步：有分母的先去分母，
第二步：去分母后，有括号的先去括号，
第三步：移项，将含有未知数的项改变符号后从方程的右边移到方程的左边，
将不含有未知数的项改变符号后从方程的左边移到方程的右边，
第四步：合并同类项，
第五步：方程两边同时除以未知数的系数，得方程的解。
绛旓細锛1锛夋煇涓杩愬姩闉嬬殑杩涗环涓250鍏冿紝鎸夋爣浠风殑涔濇姌閿鍞椂锛屽埄娑︾巼涓15.2%锛岃繍鍔ㄩ瀷鐨勬爣浠锋槸澶氬皯锛熻В鏋愶細鏈鏈夊涓嬬殑绛夐噺鍏崇郴锛氭爣浠穢90%=鐜板敭浠 锛堝敭浠-杩涗环锛壝疯繘浠穢100%=鍒╂鼎鐜 瑙ｈ锛氳繍鍔ㄩ瀷鐨勬爣浠锋槸x鍏冿紝鏍规嵁棰樻剰寰楋細锛90%x-250锛壝250锛15.2 涔熷彲浠ョ敱鍞环-杩涗环=鍒╂鼎杩欎竴绛夐噺鍏崇郴鍒鏂圭▼锛90%...
绛旓細瑙ｏ細璁続鍗曚环x鍏冿紝B鍗曚环x+1鍏 绛夐噺鍏崇郴锛2鐡禔鐨勪环鏍+3鐡禕鐨勪环鏍=13鍏 2x+3(x+1)=13 2x+3x+3=13 5x=10 x=2 x+1=2+1=3 绛旓細A鍗曚环2鍏冿紝B鍗曚环3鍏 6.6.鏈変竴鏍圭绔垮拰涓鏉＄怀瀛愶紝缁冲瓙姣旂绔块暱0.5绫筹紝灏嗙怀瀛愬鎶樺悗.瀹冩瘮绔圭鐭簡0.5绫筹紝姹傜绔垮拰缁冲瓙鍚勬槸澶氬皯锛熻В锛氳缁冲瓙闀縳绫筹紝...
绛旓細瑙ｏ細璁捐繘浠蜂负姣忎欢x鍏 宸茬煡 鍟嗗搧鐨勯浂鍞环涓烘瘡浠600鍏冿紝鍟嗗簵鎸夐浂鍞环鐨勫叓鎶橀檷浠凤紝骞惰鍒20鍏冮攢鍞紝鍒欓攢鍞殑浠锋牸涓 600*0.8-20=480-20=460鍏 浠嶅彲鑾峰緱15%锛堢浉瀵逛簬杩涗环锛夛紝鍒欐湁 x锛1+15%锛=460 鍗 1.15x=460 x=400鍏 杩涗环涓烘瘡浠400鍏 ...
绛旓細1 x(1+20%)*90%=270 瑙ｏ細鍘熷紡=0.18x=270 x=1500 2 2500*锛100000/2500+x)*80%=1000000 瑙ｏ細鍘熷紡=2000*(100000+2500x)=1000000 x=-399.8
绛旓細璁続B璺▼涓簒锛屾寜鐢层佷箼涓や汉鎵鑺辩殑鏃堕棿鐩稿悓鍒楀紡锛歺/4=2.5+2.5*4/6+15/60+x/6 x/4=2.5+5/3+1/4+x/6 3x=30+20+3+2x 瑙ｅ緱锛歺=53km
绛旓細2(x+1)>5x 绛旀锛歺<2/33(x-2)<2x-17绛旀锛歺<-114(y-3)+7<-13-3(2y+1)绛旀锛歽<-1.110-2(x-1)<3(x-1)-25绛旀锛歺>82x-8<4x-7绛旀锛歺>-1/22(x+9)>3(1-x)绛旀锛歺>-31-7(y+2)<2(y-1)+5绛旀锛歽>16/9x-1/2(x+1)>10绛旀锛歺>211-x/4<5+(x-2)/6...
绛旓細锛1锛 宸茬煡x鐨勪笁鍊嶄簬x-6鐨勫肩浉绛夛紝姹倄锛堜篃瑕佸儚涓婇潰涓鏍峰啓锛夎В锛氫緷棰樻剰寰楋細3x=x-6 绉婚」锛屽緱锛3x-x=-6 鍚堝苟鍚岀被椤癸紝寰楋細2x=-6 绯绘暟鍖栦负1,寰楋細x=-3 鎵浠ワ紝x鏄-3.锛2锛夊凡鐭=-2鏄叧浜巠鐨勬柟绋嬶紙y+m锛-锛坢y-3锛=3y鐨勮В锛屾眰m鐨勫 瑙ｏ細灏唝=-2浠ｅ叆鍏充簬y鐨勬柟绋锛坹+m锛-锛坢y...
绛旓細瑙ｈ鎸戝湡x浜猴紝鍒欐姮鍦熺殑2锛40-x锛変汉 2x+2锛40-x锛壝2=60 2x+40-x=60 x=20 2锛40-x锛=2脳锛40-20锛=40浜 20+40=60浜 绛斿弬鍔犳娆℃鏍戞椿鍔ㄧ殑瀛︾敓鏈60浜
绛旓細鍥炵瓟锛17-3x=5 3x=17-5 3x=12 x=4
绛旓細6.涓鍏冧竴娆′笉绛夊紡缁鐨勮В銆佽В涓鍏冧竴娆′笉绛夊紡缁(鍦ㄦ暟杞翠笂琛ㄧず瑙ｉ泦) 鏂圭▼鐨勫簲鐢ㄩ棶棰樼殑鏁欏鍙互璇磋疮绌夸簡鏁翠釜灏忓楂樺勾绾у娈靛拰鍒濅腑瀛︽,鍦ㄥ鐢熺殑鏁板瀛︿範娲诲姩涓崰鏈夌浉褰撻噸瑕佺殑鍦颁綅(鏁翠釜鍒濅腑娈垫柟绋嬪強鍏跺簲鐢ㄩ鐨勬暀瀛﹀鏃朵负41瀛︽椂,绾﹀崰鏁翠釜鍒濅腑鏁板瀛︽椂鐨11.5%),鑰涓鍏冧竴娆℃柟绋搴旂敤棰樼殑鏁欏,鍙堟槸鎵鏈夋柟绋嬪簲鐢ㄩ鏁欏涓渶鍩虹...
