Question

If x=2+√3, find the value of x³+1/x³​

Answer 1

$\tt{here \: is \: your \: answer} \\ \tt{given : \star \: x = 2 + \sqrt{3} } \\ \tt{t oo \: find : \star \: {x}^{3} + \frac{1}{ {x}^{3} } } \\ \tt{sol {}^{n} : (2 + \sqrt{3} ) {}^{3} + \frac{1}{(2 + \sqrt{3 {}^{} } ) {}^{3} } } \\ \tt{8 + ( \sqrt{3}) {}^{3} + 3(2)( \sqrt{ 3} )(2 + \sqrt{3} ) + \frac{1}{8 + ( \sqrt{3}) {}^{3} + 3(2)( \sqrt{ 3} )(2 + \sqrt{3} } } \\ \tt{8 + 3 \sqrt{3} + 6 \sqrt{3} (2 + \sqrt{3}) + \frac{1}{8 + 3 \sqrt{3} + 6 \sqrt{3} (2 + \sqrt{3} ) }} \\ \tt{8 + 15 \sqrt{3} + 18 + \frac{1}{8 + 15 \sqrt{3} + 18 } } \\ \tt{26 + 15 \sqrt{3} + \frac{1}{26 + 15 \sqrt{3}} } \\ \tt{ \frac{(26 + 15 \sqrt{3} ) {}^{2} + 1 } {26 + 15 \sqrt{3} } } \\ \tt{ \frac{26 {}^{2} + 225 \times 3 + 1}{26 + 15 \sqrt{3} } } \\ \tt{ \frac{676 + 675 + 1}{26 + 15 \sqrt{3} } } \\ \tt{ \frac{1352}{26 + 15 \sqrt{3} } }$

Hope you get your answer...