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

1.	X+1/x=3 then the value of x^8+1/x^8
Answer» $\huge{ \sf{ \red{ \mid{ \underline{ \overline{ \purple{work \: out..}}}}}}}$ $\large{ \bold{ \red{ \underline{ \underline{Question..}}}}}$ $\sf{x+1/x=3 \: then \: the \: value \: of \: x^8+1/x^8}$ $\large{ \bold{ \green{ \underline{ \underline{solution..}}}}}$ $\large{ \bold{ \red{ \underline{ \underline{Given..}}}}}$ $\sf{x + \frac{1}{x} = 3}$ $\large{ \bold{ \red{ \underline{ \underline{to \: find..}}}}}$ $\sf{ {x}^{8} + \frac{1}{ {x}^{8} } }$ $\large{ \to \:x + \frac{1}{x} = 3} \\ \\ \large{ \sf{\to \: (x + \frac{1}{x} ) {}^{2} = 9}} \\ \\ \large{ \sf{ \to \: {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9}} \\ \\ \large{ \sf{ \to \: {x}^{2} + \frac{1}{ {x}^{2} } = 7}} \\ \\ \sf{ \green{similarly...}} \\ \large{ \sf{ \to \: ( {x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = 49}} \\ \\ \large{ \sf{ \to \: {x}^{4} + \frac{1}{ {x}^{4} } = 49 - 2 = 47}} \\ \sf{ \green{then...}} \\ \large{ \sf{ \to \: ({x}^{4} + \frac{1}{ {x}^{4} } ) {}^{2} = 2401}} \\ \\ \large{ \sf{ \to \: {x}^{8} + \frac{1}{ {x}^{8} } = 2401 - 2 = 2399}} \\ \\ { \red{\boxed{ \large{required \: answer - 2399}}}}$ $\large{ \bold{ \purple{nothing \: beats \: a \: great \: smile..}}}$ $\large{ \bold{ \purple{ so \: keep \: smililing...}}}$

Answer»

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

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

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

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

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

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

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

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

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

$\large{ \bold{ \purple{nothing \: beats \: a \: great \: smile..}}}$

$\large{ \bold{ \purple{ so \: keep \: smililing...}}}$

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

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