已知,m²-5m-1=0,求2m²-5m+1/m²的值.
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![已知,m²-5m-1=0,求2m²-5m+1/m²的值.](/uploads/image/z/2586600-0-0.jpg?t=%E5%B7%B2%E7%9F%A5%2Cm%26%23178%3B-5m-1%3D0%2C%E6%B1%822m%26%23178%3B-5m%2B1%2Fm%26%23178%3B%E7%9A%84%E5%80%BC.)
已知,m²-5m-1=0,求2m²-5m+1/m²的值.
已知,m²-5m-1=0,求2m²-5m+1/m²的值.
已知,m²-5m-1=0,求2m²-5m+1/m²的值.
显然,m不为0,否则条件不成立.
∵m^2-5m-1=0, ∴2m^2-10m=2, ∴2m^2-5m=2+5m.
∵m^2-5m-1=0, ∴1-5/m-1/m^2=0, ∴1/m^2=1-5/m.
∵m^2-5m-1=0, ∴m-5-1/m=0, ∴m-1/m=5, ∴5m-5/m=25.
于是:
2m^2-5m+1/m^2=(2+5m)+(1-5/m)=3+(5m-5/m)=3+25=28.