Question

已知x的平方-5x-1=0,求x-1/x,x的平方/x的四次方+x的平方+1的值

Answer 1

x²-5x-1=0 两边同时除以x得

x-5-1/x=0

x-1/x=5

x²/(x的4次方+x²+1)

=1/(x²+1+1/x²)

=1/[(x²-2+1/x²)+3]

=1/[(x-1/x)²+3]

=1/(5²+3)

=1/(25+3)

=1/28

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