Question

已知x^2+3x-1=0,求x^4+1/x^4的值

如题

Answer 1

x^2+3x-1=0
x+3-1/x=0
x-1/x=-3
(x-1/x)²=9
x²+1/x²=11
(x²+1/x²)²=121
x^4+1/x^4=119

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Answer 2

x^2+3x-1=0
除以x得
x-1/x=-3
平方得
x^2+1/x^2=9+2=11
所以
x^4+1/x^4=(x^2+1/x^2)^2-2=11^2-2=121-2=119

Answer 3

x^2+3x-1=0(等式两边同除以x)
-->x-1/x=-3(等式两边同时平方)
-->x^2+1/x^2-2x*1/x=9
-->x^2+1/x^2=11(等式两边同时平方)
-->x^4+1/x^4+2=121
-->x^4+1/x^4=119

Answer 4

x^2+3x-1=0
两边同除以x^2得
x+1/x=3
x^2+1/x^2=(x+1/x)^2-2=7
x^4+1/x^4=(x^2+1/x^2)^2-2=47

Answer 5

119