Question

已知x²+2x-1=0,求下列式子的值:(1)x-1/x.(2)x²+1/x²;(3)(x²)²＋1/(x²)&su

Answer 1

x²+2x-1=0
X+2-1/X=0
X-1/X=-2 :(1)x-1/x=-2
(x-1/x)^2=4
x^2+1/x^2-2x*1/x=4
x^2+1/x^2-2=4
x^2+1/x^2=6 .(2)x²+1/x²=6
(x^2+1/x^2)^2=36
x^4+1/x^4+2x^2*1/x^2=36
x^4+1/x^4+2=36
x^4+1/x^4=34 ;(3)(x²)²＋1/(x²)^2=34

Answer 2

X^2+2x-1=0 两边除以x（x显然不为0）
x+2-1/x=0,则(1)x-1/x=-2
(1)式平方，有：(x-1/x)^2=x^2-2+1/x^2=4
则(2)x^2+1/x^2=6
(2)式平方，有：(x^2+1/x^2)^2=x^4+2+1/x^4=36
则(3)x^4+1/x^4=34