Question

x+1/x=3 then the value of x^8+1/x^8

Answer 1

$\huge{ \sf{ \red{ \mid{ \underline{ \overline{ \purple{work \: out..}}}}}}}$

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$\sf{x+1/x=3 \: then \: the \: value \: of \: x^8+1/x^8}$

$\large{ \bold{ \green{ \underline{ \underline{solution..}}}}}$

$\large{ \bold{ \red{ \underline{ \underline{Given..}}}}}$

$\sf{x + \frac{1}{x} = 3}$

$\large{ \bold{ \red{ \underline{ \underline{to \: find..}}}}}$

$\sf{ {x}^{8} + \frac{1}{ {x}^{8} } }$

$\large{ \to \:x + \frac{1}{x} = 3} \\ \\ \large{ \sf{\to \: (x + \frac{1}{x} ) {}^{2} = 9}} \\ \\ \large{ \sf{ \to \: {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9}} \\ \\ \large{ \sf{ \to \: {x}^{2} + \frac{1}{ {x}^{2} } = 7}} \\ \\ \sf{ \green{similarly...}} \\ \large{ \sf{ \to \: ( {x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = 49}} \\ \\ \large{ \sf{ \to \: {x}^{4} + \frac{1}{ {x}^{4} } = 49 - 2 = 47}} \\ \sf{ \green{then...}} \\ \large{ \sf{ \to \: ({x}^{4} + \frac{1}{ {x}^{4} } ) {}^{2} = 2401}} \\ \\ \large{ \sf{ \to \: {x}^{8} + \frac{1}{ {x}^{8} } = 2401 - 2 = 2399}} \\ \\ { \red{\boxed{ \large{required \: answer - 2399}}}}$

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