代数式求值练习题及答案 七年级数学代数式求值练习题
\u521d\u4e00\u4e0a\u5b66\u671f\u7684\u4ee3\u6570\u5f0f\u6c42\u503c\u9898\uff08\u542b\u7b54\u6848\uff09\u521d\u4e00\u6570\u5b66\u7ade\u8d5b\u4e13\u9898\u57f9\u8bad\u4ee3\u6570\u5f0f\u6c42\u503c\u89e3\u9898
\u5982\u679cx+y=2z,\u4e14x\u4e0d\u7b49\u4e8ey\uff0c\u52192x/x-y+y/y-z=?\uff08/\u662f\u5206\u6570\u7ebf,\u524d\u6570\u662f\u5206\u5b50\uff09
A 4 B 6 C 8 D10
\u82e5a+b+c=0\uff0c\u5219a(1/b+1/c)+b(1/a+1/c)+c(1/b+1/a)\u7684\u503c\u4e3a_______
\u8bbem\u76842\u6b21\u65b9+m-1\uff1d0\uff0c\u5219m\u76843\u6b21\u65b9+2\u4e58\u4ee5m\u76842\u6b21\u65b9+1997\uff1d______
\u5df2\u77e5a-b=1,c-a=2,\u5219\uff08a-b)\u76843\u6b21\u65b9+(c-d)\u76843\u6b21\u65b9+\uff08c\uff0da\uff09\uff1d________
\u5df2\u77e5a\u4e58\u4ee5b\u76842\u6b21\u65b9\uff1d6\uff0c\u6c42ab(a\u4e58\u4ee5b\u76843\u6b21\u65b9+a\u76842\u6b21\u65b9\u4e58\u4ee5b\u76845\u6b21\u65b9-b\uff09\uff1d________
\u53c2\u8003\u7b54\u6848\uff1a
1.z=(x+y)/2,\u4ee3\u5165\u6240\u6c42\u5f0f\uff0c\u53ef\u5f972x/(x-y) + y/[y-(x+y)/2] \u6574\u7406\u53ef\u5f97
2x/(x-y) + 2y/(y-x) = 2(x-y)/(x-y) =2;
2.\u5c55\u5f00\u6240\u6c42\u5f0f\u5f97 a/b + a/c + b/a + b/c + c/b + c/a = (b+c)/a + (a+c)/b + (a+b)/c
= (-a)/a + (-b)/b + (-c)/c = -3;
3.\u6240\u6c42\u5f0f m3 + 2 m2 +1997= m(m2+m-1) + m2 +m-1 +1998 = 1998;
4.(a-b)+(c-a)=c-b=3 \u6240\u6c42\u5f0f=1x1x1+ 3x3x3 +2=30;
5.\u6240\u6c42\u5f0f\u5c55\u5f00 a2b4+a3b6-ab2=(ab2)2+(ab2)3-(ab2)=6x6+6x6x6-6=246;
\u6ce8\uff1a3,5\u9898\u4e2d\u5b57\u6bcd+\u6570\u5b57n\u8868\u793a\u8be5\u5b57\u6bcd\u7684n\u6b21\u65b9
\u5982m3\u8868\u793am\u76843\u6b21\u65b9 a2b4\u8868\u793aa\u76842\u6b21\u65b9\u4e58b\u76844\u6b21\u65b9
(ab2)2 \u8868\u793aa\u4e58b\u7684\u4e8c\u6b21\u65b9\u6240\u5f97\u79ef\u76842\u6b21\u65b9
\u628az=(x+y)/2\u4ee3\u5165\u5e76\u6574\u7406
2x/x-y+y/y-z=2x/(x-y)+y/[y-(x+y)/2]=2(x-y)/(x-y) =2
\u539f\u5f0f\u5c55\u5f00\u5e76\u4ee3\u5165a+b+c=0\uff08\u6574\u7406\u5f0f\uff09a(1/b+1/c)+b(1/a+1/c)+c(1/b+1/a)=(-a)/a + (-b)/b + (-c)/c = -3
m^3+2m^2+1997=m^2(m-2)+1997=m-m^2+1997=m-m+1+1997=1998
(a-b)+(c-a)=c-b=3\u4ee3\u5165(a-b) ^3+(c-b)^3+\uff08c\uff0da\uff09\uff1d1+27+2=30
b^2=6/a\u4ee3\u5165\u5f97 ab(6b+36b-b)=41ab^2=41*6=246
\u4ee3\u6570\u5f0f\u57fa\u672c\u5185\u5bb9\u7ec3\u4e60\u9898\uff1a(\u7b54\u6848\u90e8\u5206)
1\u3001\u4e0b\u5217\u5f0f\u5b50\u4e2d\u4ee3\u6570\u5f0f\u7684\u4e2a\u6570\u6709 8 \u4e2a\uff0c\u5206\u5f0f\u6709 1 \u4e2a\uff0c\u65e0\u7406\u5f0f\u6709 2 \u4e2a\u3002
5\u3001 ba \u300134 a-2b \u3001S =vt \u30013\u03c0 \u3001m\u30013x-6>5\u3001 -5x2 y z10\u3001a+3a2-1 \u3001x2+1.
2\u3001\u591a\u9879\u5f0f1-x24 \u7684\u6700\u9ad8\u6b21\u9879\u7cfb\u6570\u662f - 14 .
3\u3001\u82e5a+b+c=0,\u5316\u7b80a(1b + 1c )+b(1c + 1a )+ c(1a + 1b )= -3
4\u3001\u5982\u679c\u67092007\u540d\u5b66\u751f\u6392\u6210\u4e00\u5217\uff0c\u63091\u30012\u30013\u30014\u30015\u30014\u30013\u30012\u30011\u30012\u30013\u30014\u30015\u30014\u30013\u30012\u30011\u2026\u2026\u7684\u89c4\u5f8b\u62a5\u6570\uff0c\u90a3\u4e48\u7b2c2007\u540d\u5b66\u751f\u6240\u62a5\u7684\u6570\u662f 3 \uff0e
5\u3001\u4e0b\u5217\u5404\u5f0f\u4e2d\u4e8c\u6b21\u6839\u5f0f\u7684\u4e2a\u6570\u6709 5 \u4e2a.
\u2460-3 \u2461m2+1 \u246227 \u2463-x2-1 \u2464-(-3)3 \u2465a+1 (a<-2) \u2466m2-2m+7 \u2467 16
6\u3001\u51fd\u6570y = 2x+31-x+1 \u7684\u81ea\u53d8\u91cfx\u7684\u53d6\u503c\u8303\u56f4\u662f x\u2265-1\u4e14x\u22600 .
7\u3001\u82e5\u4ee3\u6570\u5f0fx+1x+2 \u00f7 x+3x+4 \u6709\u610f\u4e49\uff0c\u5219x\u7684\u53d6\u503c\u8303\u56f4\u662f x\u2260-2\u4e14x\u2260-3\u4e14x\u2260-4 .
8\u3001\u7ed9\u51fa\u7684\u4e0b\u5217\u8ba1\u7b97\u6216\u5316\u7b80\uff1a\uff081\uff09(a2)4= a6\uff0c\uff082\uff09(-3a)3 =-27 a3
\uff083\uff092-2= 14 \uff0c \uff084\uff09a2 -2a=-3a(a<0)\u5176\u4e2d\u6b63\u786e\u4e2a\u6570\u6709\uff08 C \uff09
A\uff0e1\u4e2a B.2\u4e2a C.3\u4e2a D.4\u4e2a
9\u3001\u5df2\u77e5a\u3001b\u662f\u6b63\u6574\u6570\uff0c\u4e14a + b = 1998 ,\u5219a+b= 1110 .
10\u3001\u5982\u679c\u4e8c\u6b21\u4e09\u9879\u5f0f3x2 \u2013 4x +2k\u5728\u5b9e\u6570\u8303\u56f4\u5185\u603b\u80fd\u5206\u89e3\u6210\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u7684\u4e58\u79ef\uff0c\u5219k\u7684\u53d6\u503c\u8303\u56f4\u662f k\u2264 23 .
11\u3001\u6570\u5b66\u6e38\u620f\uff1a\u89c4\u5b9a\uff0c\u5bf9\u4efb\u610f\u5b9e\u6570\u5bf9\uff08a\uff0cb\uff09\u6309\u89c4\u5219\u4f1a\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\u5b9e\u6570\uff1aa2+b+1.\u4f8b\u5982\u628a\uff085\uff0c\u20131\uff09\u653e\u5165\u5176\u4e2d\uff0c\u5c31\u4f1a\u5f97\u523052+(\u20131)+1=25.\u73b0\u5c06\u5b9e\u6570\u5bf9(\u20133\uff0c2)\u653e\u5165\u5176\u4e2d\u5f97\u5230\u5b9e\u6570n\uff0c\u518d\u5c06\u5b9e\u6570\u5bf9\uff08n\uff0c\u20131\uff09\u653e\u5165\u5176\u4e2d\u540e\uff0c\u5f97\u5230\u7684\u5b9e\u6570\u662f 144 .
12\u3001\u5df2\u77e5 \uff0c\u5f53n=1\u65f6\uff0ca1=0\uff1b\u5f53n=2\u65f6\uff0ca2=2\uff1b\u5f53n=3\u65f6\uff0c a3=0\uff1b\u2026 \u5219a1+a2+a3+a4+a5+a6\u7684\u503c\u4e3a 6 \uff0e
13\u3001\u5206\u89e3\u56e0\u5f0f\uff1a
\u89e3\uff1a\uff081\uff09ax2 -4ax+4a \uff082\uff09a3 \u2013 a
= a(x2 -4x+4) =a(a2 \u2013 1)
= a (x-2)2 =a(a+1)(a-1)
\uff083\uff092x2+3x-6 \u22352x2+3x-6=0\u7684\u4e24\u6839\u4e3a
=2\uff08x-\u03b1\uff09(x-\u03b2) x= -3+574 \u548cx= -3-574
\u5176\u4e2d\u03b1\u3001\u03b2\u4e3a\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b \u2234 2x2+3x-6
2x2+3x-6=0\u7684\u4e24\u6839\u3002 = 2\uff08x- -3+574 \uff09(x- -3-574 )
14\u3001\u8ba1\u7b97\uff1a(1+ x2-1 x2-2x+1 )\u00f71x-1
\u89e3\uff1a\u539f\u5f0f=[1+ (x+1)(x-1) (x-1)2 ]\u00d7(x-1)
=(1+ x+1x-1 )\u00d7(x-1)
= 2xx-1 \u00d7(x-1)
= 2x
15\u3001\u5148\u5c06\u5f0f\u5b50\uff081 + 1x \uff09\u00f7x2-1 x2 \u5316\u7b80\uff0c\u7136\u540e\u8bf7\u4f60\u81ea\u9009\u4e00\u4e2a\u7406\u60f3\u7684x\u503c\u6c42\u51fa\u539f\u5f0f\u7684\u503c.
\u89e3\uff1a\uff081 + 1x \uff09\u00f7x2-1 x2 \u5bf9\u4e8ex\u7684\u53d6\u503c\u53ef\u81ea\u5df1\u9009\u53d6\uff0c
= x+1x \u00d7 x2 (x+1)(x-1) \u4f46x\u4e0d\u53ef\u53d60\u30011\u548c-1,\u5426\u5219
= xx-1 \u65e0\u610f\u4e49\u3002
16\u3001\u5df2\u77e5\uff0ca >0\uff0cb|a|>|b|.
\u5316\u7b80\uff1a|a+b| + |a+c| \u2013 |c-b|
\u89e3\uff1a\u2235a >0\uff0cb|a|>|b|
\u2234 a + b > 0 , a + c < 0 ,c \u2013 b < 0
\u2234 |a+b| + |a+c| \u2013 |c-b|
= a+b-(a+c)+(c-b)
= a+b-a-c+c-b
=0
\u8fd9\u53ef\u662f\u6211\u82b1\u94b1\u4e70\u7684\u54e6\uff0c\u8ba4\u771f\u505a\uff0c\u7b54\u6848\u6211\u6253\u4e0a\u4e86\u3002
\u6ee1\u610f\u5417?
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