x+x^-1=3,则x^2+x^-2=?

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x+x^-1=3,则x^2+x^-2=?x+x^-1=3,则x^2+x^-2=?x+x^-1=3,则x^2+x^-2=?x+x^-1=3,两边平方,x^2+2+x^-2=9,x^2+x^-2=7x^2

x+x^-1=3,则x^2+x^-2=?
x+x^-1=3,则x^2+x^-2=?

x+x^-1=3,则x^2+x^-2=?
x+x^-1=3,两边平方,x^2+2+x^-2=9,x^2+x^-2=7

x^2+x^-2=(x+1/x)^2-2=3^2-2=7

对原式两边同时平方....
变成x^2+x^-2 +2=9
∴x^2+x^-2=7

x+x^-1=3则（x+x^-1）²=x²+2*x*x^-1+x^-2=x^2+x^-2+2=9
所以x^2+x^-2=7

x+1/x=3，则有：x^2+1+x^-(2)=(x+1/x)^2=9，
所以x^2+x^-2=8

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