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Find \(m^2+\frac{1}{m^2}\) if \(m+\frac{1}{m} =9\).

 Jul 9, 2020
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\(\left(m + \dfrac1m\right)^2 = 9^2 \\ m^2 + 2m\cdot \dfrac1m + \left(\dfrac1m\right)^2 = 81\\ m^2 + \dfrac1{m^2} = 81-2 = \boxed{79}\)

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 Jul 11, 2020

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