1.

If \({x^2} - \sqrt 3 x + 1 = 0\), then \(\left( {{x^3} + {x^{ - 3}}} \right)\) is equal to:

Answer» Correct Answer - Option 1 : 0

Given:

\({x^2} - √ 3 x + 1 = 0\)

Concept used:

Algebra

Calculation:

Divide the given equation by x

⇒ \(x + \frac{1}{x} = √ 3 \)

We need to find (x + 1/x)3

Let (x + 1/x) = k = √3

\({\left( {x + \frac{1}{x}} \right)^3} = {x^3} + \frac{1}{{{x^3}}} + 3k\)

\({x^3} + \frac{1}{{{x^3}}} = {\left( {x + \frac{1}{x}} \right)^3} - 3k\)

\({x^3} + \frac{1}{{{x^3}}} = {\left( {\sqrt 3 } \right)^3} - 3k\)

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

∴ \({x^3} + \frac{1}{{{x^3}}} = 0\)


Discussion

No Comment Found

Related InterviewSolutions