已知(a+1)^2+(b-3)^2=0,求ab已知│x+2│+(y-1)^2+(z-1)^4=0,求x^yz的值已知│x+2│+(y-1)^2=0,求xy已知x^2-5x+1=0,求x^4+1/x^4的值已知x+y=5,x-y=4,求值：(1)x^2+y^2;(2)xy已知x^2-y^2=20,x-y=4,求x+y的值

Question

已知(a+1)^2+(b-3)^2=0,求ab
已知│x+2│+(y-1)^2+(z-1)^4=0,求x^yz的值
已知│x+2│+(y-1)^2=0,求xy
已知x^2-5x+1=0,求x^4+1/x^4的值
已知x+y=5,x-y=4,求值：(1)x^2+y^2;(2)xy
已知x^2-y^2=20,x-y=4,求x+y的值

Answer 1

1、a+1=0
b-3=0
∴a=-1
b=3
∴ab=-3
2、x+2=0
y-1=2
z-1=0
∴x=-2
y=1
z=1
∴x^yz=-2
3、x+2=0
y-1=0
∴x+2=0
y-1=0
∴x=-2
y=1
xy=-2
4、x-5+1/x=0 两边除以x
∴x+1/x=5
两边平方得
x²+2+1/x²=25
∴x²+1/x²=23
两边再平方得
x^4+2+1/x^4=529
∴x^4+1/x^4=527
5、x+y=5
∴(x+y)²=25
x²+2xy+y²=25 (3)
x-y=4
∴(x-y)²=16
x²-2xy+y²=16 (4)
(3)+(4)得
2x²+2y²=41
∴x²+y²=41/2
(3)-(4)得
4xy=9
∴xy=9/4
6、x²-y²=20
∴(x+y)(x-y)=20
∵x-y=4
∴4(x+y)=20
x+y=5