Question

if x=9+4√5 find the value of x cube +1/x cube

Answer 1

.HEYYY MATE...
THANKS FOR THE QUESTION....
UR ANS IS HERE IN THE ATTACHMENT...
HOPE IT HELPS U....
IF IT IS HELPFUL TO YOU PLZZZ MARK ME BRAINLIEST....

Answer 2

$x = 9 + 4 \sqrt{5} \\ \frac{1}{x} = \frac{1}{9 + 4 \sqrt{5} } = \frac{9 - 4 \sqrt{5} }{(9 + 4 \sqrt{5} )(9 - 4 \sqrt{5} )} \\ \frac{9 - 4 \sqrt{5} }{81 - 80} = 9 - 4 \sqrt{5} \\ x + \frac{1}{x} = (9 + 4 \sqrt{5} ) + (9 - 4 \sqrt{5} ) = 18$
${x}^{3} + \frac{1}{ {x}^{3} } = {(x + \frac{1}{x} )}^{3} - 3(x + \frac{1}{x} ) \\ = {18}^{3} - 3 \times 18 = 5778$