Question

$x - \frac{1}{x} = 7 \: \: evaluate \: {x}^{4} + \frac{1}{ {x}^{4} }$
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Answer 1

Answer:

2599

Step-by-step explanation:

$\bold{Given: \: x - \frac{1}{x} = 7. } \\ \\ \bold{Squaring \: both \: the \: sides.then} \\ \\ \bold{ \bigg( {x - \frac{1}{x}}\bigg)^{2} = {7}^{2} } \\ \\ \bold{ \implies{ \bigg( {x}^{2} + \frac{1}{ {x}^{2} } - 2 \times x \times \frac{1}{x} \bigg) = 49}} \\ \\ \bold{ \implies{ \bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg) = 49 + 2 = 51}} \\ \\ \bold{Again \: squaring \: both \: the \: sides.Then,} \\ \\ \bold{ \implies{ {\bigg( {x}^{2} + \frac{1}{ {x}^{2} } \bigg) }^{2} = {51}^{2} }} \\ \\ \bold{ \implies{ \bigg( {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } \bigg) = 2601.}} \\ \\ \green{\bold{ \implies{ \underline{ \bigg( {x}^{4} + \frac{1}{ {x}^{4} } \bigg) = 2601 - 2 = \boxed{2599}.}}}}$