Question

if x + 1/x = 7 find x4 + 1/x4.

Answer 1

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Here is your answer

$(x + \frac{1}{x} ) {}^{2} = 7 {}^{2} \\ {x}^{2} + \frac{1}{x {}^{2} } + 2 = 49 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 49 - 2 \\ again \: squaring \\ ( {x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = (47) {}^{2} \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 2209 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 2209 - 2 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 2207$

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