Question

x+1_x=7 find the value of x3+1_x3=?​

Answer 1

$\sf{given \: \: x + \frac{1}{x} = 7}$

cubing on both sides

$\sf{ \: \: {(x + \frac{1}{x})}^{3} = {7}^{3} }$

$\sf{ \: \: { {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} )}= 343 }$

$\sf{\: \: { {x}^{3} + \frac{1}{ {x}^{3} } + 3(7)}= 343 }$

$\sf{ \: \: { {x}^{3} + \frac{1}{ {x}^{3} } + 21}= 343 }$

$\sf{ \: { {x}^{3} + \frac{1}{ {x}^{3} } }= 343 - 21}$

$\fbox{\sf{ \: { {x}^{3} + \frac{1}{ {x}^{3} } }= 322}}$

Answer 2

A pleasure night my dear friend,

Please refer to the attachment for answer.

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