Question

find X(cube)―1/x(cube) if X=4+√15

Answer 1

Hello Mate!

$if \: x = 4 + \sqrt{15} \\ \frac{1}{x} = \frac{1}{4 + \sqrt{15} } \times \frac{4 - \sqrt{15} }{4 - \sqrt{15} } \\ \frac{4 - \sqrt{15} }{16 - 15} = 4 - \sqrt{15} \\ {x}^{3} = {(4 + \sqrt{15}) }^{3} \\ = {4}^{3} + { \sqrt{15} }^{3} + 3 {(4)}^{2} ( \sqrt{15} ) + 3(4)( { \sqrt{15} )}^{2} \\ = 64 + 15 \sqrt{15} + 48 \sqrt{15} + 180 \\ = 244 + 63 \sqrt{15} \\ \frac{1}{ {x}^{3} } = {(4 - \sqrt{15} )}^{3} \\ {4}^{3} - { \sqrt{15} }^{3} - 3 {(4)}^{2} \sqrt{15} + 3(4)( { \sqrt{15}) }^{2} \\ = 64 - 15 \sqrt{1} - 48 \sqrt{15} + 180 \\ = 244 - 63 \sqrt{15} \\ {x}^{3} - \frac{1}{ {x}^{3} } = 244 + 63 \sqrt{15} - (244 - 63 \sqrt{15} ) \\ = 126 \sqrt{15}$
Formulas used = ( a + b )^3 = a^3 + b^3 + 3a^2b + 3ab^2
( a - b )^3 = a^3 - b^3 - 3a^2b + 3ab^2

Hope it helps☺!✌

Ping me out if any confusion