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已知m2-5m-1=0,求2m2-m+1/m2的值
人气:438 ℃ 时间:2020-04-25 13:43:23
解答
m^2-5m-1=0
m≠0,两边同除以m,得
m-1/m=5
(m-1/m)²=25
m²+1/m²-2=25
m²+1/m²=27
m^2-5m=1
2m^2-5m+(1/m^2)
=m²+m²-2m+(1/m²)
=m²+(1/m²)+1
=27+1
=28
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