Quantitative Aptitude :: Square Root and Cube Root - Discussion

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Explanation:
\(x =\frac{(\sqrt3 + 1)}{(\sqrt3-1)} \times\frac{(\sqrt3 + 1)}{(\sqrt3+1)}= \frac{(\sqrt3 + 1)^2}{3-1} = \frac{3 + 1 + 2\sqrt3}{2} = 2 +\sqrt 3.\)

\(y = \frac{(\sqrt3 - 1)}{(\sqrt3+1)} \times \frac{(\sqrt3 - 1)}{(\sqrt3-1)}= \frac{(\sqrt3 - 1)^2}{3-1} = \frac{3 + 1 - 2\sqrt3}{2} = 2 -\sqrt 3.\)

\(x^2 + y^2 = (2 + \sqrt3)^2 + (2 - \sqrt3)^2\) = 2(4 + 3) = 14