Question

If x =2 root 5+3root 2/2 root 5 - root 2 find value of x cube +1/X cube ​

Answer 1

Step-by-step explanation:

$x = \frac{2 \sqrt{5 } + 3 \sqrt{2} }{2 \sqrt{5} - 3\sqrt{2} } \times \frac{2 \sqrt{5} + 3\sqrt{2} }{2 \sqrt{5} + 3\sqrt{2} } \\ \\ = \frac{20 + 6 \sqrt{10} + 6 \sqrt{10} + 18}{ {(2 \sqrt{5}) }^{2} - {( 3\sqrt{2} )}^{2} } \\ \\ = \frac{38 + 12\sqrt{10} }{2} = 19 + 6 \sqrt{10} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = {(19 + 6 \sqrt{10}) }^{3} + \frac{1}{ {(19 + 6 \sqrt{10} )}^{3} } \\ \\ \red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$