Question

Please tell me the answer correctly with explanation​

Answer 1

Solution :

$x \: =\: (2\: +\: \sqrt{3})^{\frac{1}{3}}$

cube both side

$x^{3} \: =\: (2\: +\: \sqrt{3})^{\frac{3}{3}}$

$x^{3} \: =\: 2\: +\: \sqrt{3}$... (eq 1)

Now we reciprocal both

$\dfrac{1}{x^3}\: =\: \dfrac{1}{2\: +\: \sqrt{3}}$

$\dfrac{1}{x^3}\: =\: \dfrac{1}{2\: +\: \sqrt{3}}\times \dfrac{2\: - \: \sqrt{3}}{2\: - \: \sqrt{3}}$

$\dfrac{1}{x^3}\: =\: \dfrac{2\: - \: \sqrt{3}}{(2)^{2}\: - \: (\sqrt{3})^{2}}$

$\dfrac{1}{x^3}\: =\: \dfrac{2\: - \: \sqrt{3}}{4\: - \: 3}$

$\dfrac{1}{x^3}\: =\: \dfrac{2\: - \: \sqrt{3}}{1}$

$\dfrac{1}{x^3}\: =\: 2\: - \: \sqrt{3}$.... (eq 2)

Sum equation (1) & (2)

$x^3\: +\:\dfrac{1}{x^3}\: =\: 2\: + \: \sqrt{3}\:+\:2\: - \: \sqrt{3}$

Answer :

$x^3\: +\:\dfrac{1}{x^3}\: =\: 4$

Answer 2

Answer:

• the correct answer is 4

• Hope it helps you