零指数幂和负整指数幂已知:2x^2-3x+2=0,求x^2+x^-2的值2x的平方减3x加2等于0,求x的平方加x的-2

学习时间:2026-08-23 21:31:13 阅读：9239

零指数幂和负整指数幂已知:2x^2-3x+2=0,求x^2+x^-2的值2x的平方减3x加2等于0,求x的平方加x的-2次方的值

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2026-08-23 21:31:13

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2x^2-3x+2=0,2x^2+2=3x,x^2+1=3x/2
x^2+x^-2
=x^2+1/x^2
=(x^4+1)/x^2
=[(x^2+1)^2-2x^2]/x^2
=[(3x/2)^2-2x^2]/x^2
=[(1/4)x^2]/x^2
=1/4