Question

if x+1/x = 2 then find the value of (x)^64+(1/x)64​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{x + \frac{1}{x} = 2}$

TO DETERMINE

$\displaystyle \sf{ {x}^{64} + \frac{1}{ {x}^{64} } }$

EVALUATION

$\displaystyle \sf{x + \frac{1}{x} = 2}$

$\displaystyle \sf{ \implies \: \frac{ {x}^{2} + 1}{x} = 2}$

$\displaystyle \sf{ \implies \: {x}^{2} + 1= 2x}$

$\displaystyle \sf{ \implies \: {x}^{2} - 2x+ 1= 0}$

$\displaystyle \sf{ \implies \: {(x - 1)}^{2} = 0}$

$\displaystyle \sf{ \implies \: x = 1}$

Hence

$\displaystyle \sf{ {x}^{64} + \frac{1}{ {x}^{64} } }$

$\displaystyle \sf{ = {(1)}^{64} + \frac{1}{ {(1)}^{64} } }$

$= 1 + 1$

$= 2$

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