1..已知（x-y)^2=8,xy=2，求x^4+y^4！！ 2.已知x+1⼀x=4,求(x-1⼀x)^2 急急急！！

1.
x^4+y^4=x^4-2(xy)²+y^4+2(xy)²
=(x²-y²)²+2(xy)²
=(x-y)²(x+y)²+2(xy)²
=(x-y)²[(x-y)²+4xy]+2(xy)²
=8*[8+4*2]+2*4
=136
2.(x-1/x)²
=(x+1/x)²-4=4*4-4=12

x^4+y^4=(x^2+y^2)^2-2x^2·y^2=【(x-y)^2+2xy】-2·4=4

(x-1/x)^2 =(x+1/x)^2-4x·1/x=12

1.（x-y)^2
x^2-2xy+y^2=8
(x+y)^2=16
x^4+y^4=(x^2-y^2)^2+2(x^2)(y^2)=(x-y)^2(x+y)^2+2(xy)^2=120

2.(x-1/x)^2 =x^2-2+1/(x^2)=x^2+2+1/(x^2)-4=(x+1/x)^2-4=12

136;4

1. 由已知得：x*2+y*2=12 将这式两边平方得
（x*2+y*2）*2=144 可得：
x*4+2(x*2)(y*2)+y*4=x*4+y*4+8=144 可知：
x*4+y*4=136
2. 将已知两边平方得：
x^2+2+(1/x)^2=16 知
x^2+（1/x)^2 =14
所求的 (x-1/x)^2 = x^2-2+（1/x)^2 =14-2 =12

1..已知（x-y)^2=8,xy=2，求x^4+y^4！！ 2.已知x+1/x=4,求(x-1/x)^2 急急急！！
解：
1. x^4+y^4
=x^4-2x^2y^2+2x^2y^2+y^4
=(x^2-y^2)^2+2x^2y^2
=[(x+y)(x-y)]^2+2(xy)^2
=(x+y)^2(x-y)^2+2(xy)^2
=8(x+y)^2+8
=8(x^2-2xy+2xy+2xy)+8
=8[(x-y)^2+4xy]+8
=8*(8+4*2)+8
=136
(2)
x+1/x=4,求(x-1/x)^2
(x+1/x)^2=16
x^2+2+1/x^2=16
x^2-2+2+2+1/x^2=16
(x-1/x)^2=16-4
(x-1/x)^2=12
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