题目

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
还是第2题的题目，x^2+1/(x^2)等于多少？大哥哥大姐姐求求你们帮帮忙~

提问时间：2021-03-24

答案

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