已知x-1⼀x=2,求x^4+1⼀x^4的值

2024-12-20 15:38:26
推荐回答(3个)
回答1:

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

x^2+1/x^2=4+2=6
(x^2+1/x^2)^2=36
x^4+2+1/x^4=36
x^4+1/x^4=36-2=34

回答2:

x^4+1/x^4=(x^2-1/x^2)^2+2=[(x-1/x)^2+2]^2+2=(4+2)^2+2=36+2=38

回答3:

x-1/x=2即平方的:x^2+1/x^2=6再平方的:x^4+1/x^=34