Question

数学已知x^2-2x-1=0,求x^4+1/x^4

不会做啊~麻烦帮忙

Answer 1

x^2-2x-1=0
x不等于0,两边除以x
x-2-1/x=0
x-1/x=2
两边平方,x^2-2*x*1/x+1/x^2=x^2+1/x^2-2=4
x^2+1/x^2=6
两边平方,x^4+2*x^2*1/x^2+1/x^4=x^4+1/x^4+2=36
所以x^4+1/x^4=36-2=34

Answer 2

x^2-2x-1=0,
x^2-1=2x,
x-1/x=2,
平方
(x-1/x)^2=4,
x^2-2+1/x^2=4,
x^2+1/x^2=6,
平方
(x^2+1/x^2)=36,
x^4+2+1/x^2=36,
所以x^4+1/x^4=34

Answer 3

x^2-2x-1=0，
x-1/x=2
(x-1/x)^2=4
x^2+1/x^2=4+2=6
(x^2+1/x^2)^2=36
x^4+1/x^4=36-2=34

Answer 4

x^2-2x-1=0，
x-1/x=2
(x-1/x)^2=4
x^2+1/x^2=4+2=6
(x^2+1/x^2)^2=36
x^4+1/x^4=36-2=34