已知x2-1=4x,求x4次方+1/x4次方的值
问题描述：
已知x2-1=4x,求x4次方+1/x4次方的值
答
x2-1=4x,
x-1/x=4
(x-1/x)²=16
x²-2+1/x²=16
x²+1/x²=18
(x²+1/x²)²=324
x^4+1/x^4=322
答
x^2-4x-1=0
等式左右都除x
x-4-1/x=0
x-1/x=4
(x-1/x)^2=x^2-2+1/x^2=16
x^2+1/x^2=18
(x^2+1/x^2)^2=x^4+2+1/x^4=324
x^3+1.x^4=322
答
x²-1=4x
x-1/x=4
(x-1/x)²=16
x²+1/x²=18
x^4+1/x^4
=(x²+1/x²)²-2
=18²-2
=322
答
x^2-1=4x
x-1/x=4
(x-1/x)^2=16
x^2+1/x^2-2=16
x^2+1/x^2=18
x^4+1/x^4
=(x^2+1/x^2)^2-2
=18^2-2
=324-2
=322