Question

ifx+1/x=√3findx³+1/x³

Answer 1

(x+1/x)^2=x^2+(1/x)^2+2x×1/x
(√3)^2=x^2+1/x^2 +2
x^2+1/x^2=1
again
x^3+1/x^3=(x+1/x)(x^2+1/x^2 -x×1/x)
=√3(1-1)
=√3×0=0
is your answer

Answer 2

Heya !!!

$x + \frac{1}{x} = \sqrt{3}$

On cubing both the sides we get,

${(x + \frac{1}{x}) }^{3} = {( \sqrt{3} )}^{3} \\ \\ {(x)}^{3} + {( \frac{1}{x}) }^{3} + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 3 \sqrt{3} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3( \sqrt{3} ) = 3 \sqrt{3} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 3 \sqrt{3} - 3 \sqrt{3} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 0$

Hope this helps ☺