Question

please tell anwer.needed urgently...
will mark as brainliest​

Answer 1

[tex]\mathfrak{\huge{Answer:-}} \\ x = 2 + \sqrt{3} \\ {x}^{3} + \frac{1}{ {x}^{3} } \\ = {(2 + \sqrt{3}) }^{3} + \frac{1}{ {(2 + \sqrt{3} )}^{3} } \\ =( 8 + 3 \sqrt{3} + 12 \sqrt{3} + 18) + \frac{1}{(8 + 3 \sqrt{3} + 12 \sqrt{3} + 18) } \\ = (15 \sqrt{3} + 26) + \frac{1}{(15 \sqrt{3} + 26)} \\ = \frac{ {(15 \sqrt{3} + 26)}^{2} + 1 }{15 \sqrt{3} + 26} \\ = \frac{675 + 676 + 780 \sqrt{3} + 1 }{15 \sqrt{3} + 26 } \\ = \frac{780 \sqrt{2} + 1352 }{15 \sqrt{3} + 26} \\ = \frac{52(15 \sqrt{3} + 26) }{(15 \sqrt{3} + 26)} \\ = 52 \\ \boxed{\boxed{\bold{\large{{x}^{3} + \frac{1}{ {x}^{3} } = 52 }}}}[/tex]