Question

if x²+1\x² = 51 then find x⁴+1\x⁴

Answer 1

Given, x² + 1 / x² = 51


Squares on both sides ,


$= > {( {x}^{2} + \dfrac{1}{ {x}^{2} } )}^{2} = {51}^{2} \\ \\ \\ \\ = > {( {x}^{2}) }^{2} + (\dfrac{1}{ {x}^{2} } ) {}^{2} + 2( {x}^{2} \times \frac{1}{ {x}^{2} } ) = 2601 \\ \\ \\ \\ = > {x}^{4} + \frac{1}{ {x}^{4} } + 2 (1) = 2601 \\ \\ \\ \\ = > {x}^{4} + \frac{1}{ {x}^{4} } = 2601 - 2 \\ \\ \\ \\ = > {x}^{4} + \frac{1}{ {x}^{4} } = 2599$

Answer 2

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