Question

Evaluate ³ + 1 /x^3 when = 2 + √3.

Answer 1

Hope this helps you....

Answer 2

$Given : 2 + \sqrt{3}$

$= > \frac{1}{x} = \frac{1}{2 + \sqrt{3}}$

$= > \frac{1}{2 + \sqrt{3}} * \frac{2 - \sqrt{3}}{2 - \sqrt{3}}$

$= > \frac{2 - \sqrt{3}}{(2)^2 - (\sqrt{3})^2}$

$= > \frac{2 - \sqrt{3}}{4 - 3}$

$= > 2 - \sqrt{3}$

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$= > x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3}$

$= > x + \frac{1}{x} = 4$

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Now,

We know that (x + 1/x)^3 = (x^3 + 1/x^3) + 3 * x * 1/x(x + 1/x).

$= > (4)^3 = (x^3 + \frac{1}{x^3}) + 3(4)$

$= > 64 = x^3 + \frac{1}{x^3} + 12$

$= > 52 = x^3 + \frac{1}{x^3}$

Therefore,

$= > \boxed{x^3 + \frac{1}{x^3} = 52}}$

Hope this helps!