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# Algebra

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If , m+(1/m) = 8 then what is the value of m^4 + 1/m^4?

Jan 9, 2022

Squaring both sides, we get that $$\left(m + \frac 1m \right)^2 = 8^2$$. Expanding gives $$m^2 + \frac{1}{m^2} + 2 = 8^2$$, so hence $$m^2 + \frac{1}{m^2} = 8^2 - 2 = 62$$. Squaring both sides again, we get that $$\left(m^2 + \frac{1}{m^2}\right)^2 = 62^2$$. Expanding gives $$m^4 + \frac{1}{m^4} + 2 = 62^2$$, so hence $$m^4 + \frac{1}{m^4} = 62^2 - 2 = \boxed{3842}$$.