Question

X square + 1 by x square equals to 7 find the value of x cube + 1 by x cube

Answer 1

hey friend , here is ur ans... plz mark it as the brainliest....

Answer 2

$\rm{ given \: \: {x}^{2} + \frac{1}{ {x}^{2} } = 7 }$

$\star \rm{ {(x + \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 }$

$\implies\rm{ {(x + \frac{1}{x} )}^{2} =7+ 2 }$

$\implies\rm{ {(x + \frac{1}{x} )}^{2} =9 }$

$\implies\rm{ x + \frac{1}{x} = \sqrt{9} }$

$\implies\rm{ x + \frac{1}{x} = 3 }$

$\star \rm{ {(x + \frac{1}{x}) }^{3} = {x}^{3} + \frac{1}{ {x}^{3}} + 3(x + \frac{1}{x} )}$

$\implies \rm{ {3}^{3} = {x}^{3} + \frac{1}{ {x}^{3}} + 3(3)}$

$\implies \rm{ 27 = {x}^{3} + \frac{1}{ {x}^{3}} + 9}$

$\implies\rm{ {x}^{3} + \frac{1}{ {x}^{3}} = 27 - 9}$

$\fbox{\rm{ {x}^{3} + \frac{1}{ {x}^{3}} = 18}}$