Question

If x square + 1/x square = 9, find the value of x^4 + 1/x^4 ​

Answer 1

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$\tt5. \: if \: {x}^{2} + \frac{1}{ {x}^{2} } = 9 \: find \: the \: value \: of \: {x}^{4} + \frac{1}{ {x}^{4} }$

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$\tt \to {x}^{4} + \frac{1}{ {x}^{4} } = \blue{79}$

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$\tt \: given \: that \: {x}^{2} + \frac{1}{ {x}^{2} } = 9$

$\tt \:on \: squaring \: both \: the \: sides \: we \: get$

$\tt \to( {x}^{2} + \frac{1}{ {x}^{2} } {)}^{2} = {9}^{2}$

$\tt \: we \: will \: use \:the \: formula \\ \tt (a + b {)}^{2} = {a}^{2} + {b}^{2} + 2ab$

$\tt \to(x {}^{2} {)}^{2} + ( \frac{1}{ {x}^{2} } {)}^{2} + 2 \times \cancel{{x}^{2}} \times \frac{1}{ \cancel{{x}^{2}} } = 81$

$\tt \to {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 81$

$\tt \to {x}^{4} + \frac{1}{ {x}^{4} } = 81 - 2$

$\tt \to {x}^{4} + \frac{1}{ {x}^{4} } = \red{79}$