Question

已知x+1/x=2,求x^2+1/x^2和(x-1/x)^2

Answer 1

你好

x^2+1/x^2
=（x+1/x）^2-2x*1/x
=2^2-2
=2

(x-1/x)^2
=x^2+1/x^2-2x*1/x
=2-2
=0

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Answer 2

解：x^2+1/x^2
=x^2+1/x^2+2-2
=（x+1/x）²-2
=2²-2
=2
(x-1/x)^2
=x²-2+1/x^2
=x²+2+1/x²-2-2
=（x+1/x）²-4
=4-4
=0
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Answer 3

x^2+1/x^2=(x+1/x)^2-2*x*1/x=4-2=2

(x-1/x)^2=(x+1/x)^2-4*x*1/x=4-4=0