Question

If x=2 add √3,find the value of x^3 add 1/x^3​

Answer 1

Answer:

65/8+root 3 is answer

Do you want explanation

Answer 2

Step-by-step explanation:

$x = 2 + \sqrt{3} \\ {x}^{3} = ( {2 + \sqrt{3)} }^{3} \\ {x}^{3} = ( {2})^{3} + ( { \sqrt{3}) }^{3} + 3(2)( \sqrt{3} )(2 + \sqrt{3} ) \\ = 8 + 3 \sqrt{3} + 6 \sqrt{3} (2 + \sqrt{3} ) \\ = 8 + 3 \sqrt{3} + 12 \sqrt{3} + 18 \\ {x}^{3} = 26 + 15 \sqrt{3} \\ \frac{1}{ {x}^{3} } = \frac{1}{26 + 15 \sqrt{3} } \times \frac{26 - 15 \sqrt{3} }{26 - 15 \sqrt{3} } \\ = \frac{26 - 15 \sqrt{3} }{ ({26})^{2} - {(15 \sqrt{3} })^{2} } \\ = \frac{26 - 15 \sqrt{3} }{676 - 675} \\ \frac{1}{ {x}^{3} } = \frac{26 - 15 \sqrt{3} }{1} \\ \frac{1}{ {x}^{3} } = 26 - 15 \sqrt{3}$