已知x^2-16x-1=0,求x^2-1/(x^2)的值

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已知x^2-16x-1=0,求x^2-1/(x^2)的值已知x^2-16x-1=0,求x^2-1/(x^2)的值已知x^2-16x-1=0,求x^2-1/(x^2)的值已知x^2-16x-1=0,x-

已知x^2-16x-1=0,求x^2-1/(x^2)的值
已知x^2-16x-1=0,求x^2-1/(x^2)的值

已知x^2-16x-1=0,求x^2-1/(x^2)的值
已知x^2-16x-1=0,
x-16-1/x=0;
x-1/x=16;
(x+1/x)²=(x-1/x)²+4=256+4=260;
x+1/x=±√260=±2√65;
求x^2-1/(x^2)的值
=(x+1/x)(x-1/x)
=±2√65×16
=±32√65;
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