若x+1/x=5,则（x-1/x）²= ____步骤

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若x+1/x=5,则（x-1/x）²= ____步骤
若x+1/x=5,则（x-1/x）²= ____步骤

若x+1/x=5,则（x-1/x）²= ____步骤
(x-1/x)²
=x²-2+1/x²
=(x²+2+1/x²)-4
=(x+1/x)²-4
=5²-4
=21

(x-1/x)²
=x²-2+1/x²
=x²+2+1/x²-4
=(x+1/x)²-4
=25-4
=21

x+1/x=5
两边平方
x²+2+1/x²=25
x²+1/x²=23
所以(x-1/x)²
=x²-2+1/x²
=23-2
=21