已知x-y的算术平方根等于2,x+y的立方根等于3,求x的平方减y的平方减8的算术平方根 已知x-2的平方根是正负2,y-28的立方根是-3,求x+y...
\u5df2\u77e5x+y\u7684\u7acb\u65b9\u6839\u7b49\u4e8e-2\uff0cx-2y\u7684\u7b97\u672f\u5e73\u65b9\u6839\u7b49\u4e8e3\uff0c\u6c423x-6y\u7684\u503c(x+y)^(1/3)=-2;
x+y=-8;
(x-2y)^(1/2)=3;
x-2y=9;
y+2y=-17;
y=-17/3;
x=-7/3;
3x-6y=-7-(-34)=-7+34=27;
\u5982\u679c\u672c\u9898\u6709\u4ec0\u4e48\u4e0d\u660e\u767d\u53ef\u4ee5\u8ffd\u95ee\uff0c\u5982\u679c\u6ee1\u610f\u8bb0\u5f97\u91c7\u7eb3
\u5982\u679c\u6709\u5176\u4ed6\u95ee\u9898\u8bf7\u91c7\u7eb3\u672c\u9898\u540e\u53e6\u53d1\u70b9\u51fb\u5411\u6211\u6c42\u52a9\uff0c\u7b54\u9898\u4e0d\u6613\uff0c\u8bf7\u8c05\u89e3\uff0c\u8c22\u8c22\u3002
\u795d\u5b66\u4e60\u8fdb\u6b65
x-2=(\u00b12)²=4
x=6
y-28=(-3)³=-27
y=1
x+y=6+1=7
\u5176\u7b97\u6570\u5e73\u65b9\u6839\u662f\u221a7
得x-y=4
由x+y的立方根等于3,
得x+y=27,
解得,x=31/2,y=23/2,
x的平方减y的平方减8
=(31/2)^2-(23/2)^2-8的算术平方根
=100的算术平方根
=10
可以求出x=31/2 y=23/2
最后答案为10
X-Y=4
X+Y=27
直接把XY都能求出来了,剩下的没啥了吧?
绛旓細鐢眡-y鐨勭畻鏈钩鏂规牴绛変簬2,寰梮-y=4 鐢眡+y鐨勭珛鏂规牴绛変簬3,寰梮+y=27,瑙e緱,x=31/2,y=23/2,x鐨勫钩鏂瑰噺y鐨勫钩鏂瑰噺8 =(31/2)^2-(23/2)^2-8鐨绠楁湳骞虫柟鏍 =100鐨勭畻鏈钩鏂规牴 =10
绛旓細x鈥y鐨勫钩鏂规牴鏄璐熸牴鍙2 鈭x锛峺=2 2x+y+7鐨勭珛鏂规牴鏄2 鈭2x锛媦锛1 瑙e緱x=1, y=锛1 鈭氾箼x²锛峺²锕氾紳鈭0=0
绛旓細宸茬煡2x+y+7鐨勭珛鏂规牴鏄3 鍒2x+y+7=3鐨3娆℃柟 2脳2+y+7=27 4+y+7=27 y+11=27 y=27-11 y=16 鍒檟+y =4+16 =20 寰梮+y鐨骞虫柟鏍=卤鈭20=卤2鈭5 鍗硏+y鐨勫钩鏂硅窡涓2鈭5鎴-2鈭5
绛旓細绠楁湳骞虫柟鏍鏄浜娆℃牴鍙 鎵浠x-y=2 绔嬫柟鏍规槸涓夋鏂规牴 鎵浠-2y+3=3 鎵浠=4锛寉=2 鎵浠=鈭(4+2+3)=鈭9=3 B=(x+2y)鐨勭珛鏂规牴=(4+4)鐨勭珛鏂规牴=2 鎵浠-A鐨勭珛鏂规牴=(2-3)鐨勭珛鏂规牴=(-1)鐨勭珛鏂规牴=-1
绛旓細x-y=(鈭2)²2x+5y- 3/8=(-3/2)³鏁寸悊锛屽緱 x-y=2 (1)2x+5y=-3 (2)(1)脳5+(2)7x=7 x=1 浠e叆(1)y=x-2=1-2=-1 鈭(x²-y²)=鈭歔1²-(-1)²]=鈭(1-1)=0
绛旓細鍗斥垰(x-2)=2 x-2=2²=4 x=6 ³鈭(2x+y+4)=2 2x+y+4=2³=8 鎵浠=4-2x=-8 鍒檟²+y²=36+64=100 鎵浠骞虫柟鏍鏄10 锛坸+1)²=36 x+1=-6锛寈+1=6 x=-7锛寈=5
绛旓細y绛変簬(x-1)鐨勭畻鏈钩鏂规牴+锛1-x)鐨勭畻鏈钩鏂规牴+2 鍥犱负鏍瑰彿涓嬪繀椤绘槸澶т簬绛変簬0,鎵浠ワ細x-1>=0 1-x>=0 瑙e緱锛X=1 鎵浠ワ細Y=0+0+2=2 X^2006+Y^X=1^2006+2^1=3
绛旓細鏄殑锛岀瓟妗堝涓嬶紝鏈涢噰绾
绛旓細瑙o細鈭 y 鐨勭畻鏈钩鏂规牴鏄 2 鈭 y = 2 ² = 4 鈭 x ² - 5 = 4 x ² = 5 + 4 x ² = 9 x = 卤 3 鈭 x > 0 鈭 x = 3
绛旓細鈭(x+2)=3 鈭磝+2=9 鈭磝=7 鈭(y-1)=2 鈭磞-1=4 鈭磞=5 鈭(x-y)=鈭(7-5)=鈭2