Question

$\huge\olive{\tt{\underline{\underline{ Solve it}}}}$​

Answer 1

$\blue{\bold{\underline{\underline{Be Brainly}}}}$

Answer 2

$\huge\underline\mathfrak\pink{Question}$

$\underline\mathtt\red{Given:}$

$\huge\sf{x = \sqrt{3} + \sqrt{2} }$

$\underline\mathtt\red{To \: find:}$

$\huge\sf{x + \frac{1}{ {x}^{3} } =?}$

Now,by finding the value of x,

$\sf{ \implies \frac{1}{x} = \frac{1}{ \sqrt{3} + \sqrt{2} } }$

$\sf{ \implies \frac{1}{x} = \frac{( \sqrt{3} - \sqrt{2} )}{( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2} ) } }$

$\sf{ \implies \frac{1}{x} = \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} }$

$\sf{\implies \frac{1}{x} = \sqrt{3} - \sqrt{2} }$

Again ,by finding the value of

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

$\sf{\implies x + \frac{1}{x} = ( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2} )}$

$\sf{\implies x + \frac{1}{x} =2 \sqrt{3} }$

Hence,

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

$\sf{=(x + \frac{1}{x})^{3} - 3x. \frac{1}{x} (x + \frac{1}{x}) }$

$\sf{ =( 2 \sqrt{3})^{3} - 3(2 \sqrt{3} )}$

$\sf{ =24 \sqrt{3} - 6 \sqrt{3} }}$

$\sf{ = 18 \sqrt{3} }$

$\underline\mathtt\blue{ThankYou}$