Question

If $\dfrac{\sqrt{13-\sqrt{11}}}{\sqrt{13+\sqrt{11}}} - \dfrac{\sqrt{13+\sqrt{11}}}{\sqrt{13-\sqrt{11}}} = x - \sqrt{y}$, then $(\sqrt{y})^x = ?$}

• A. $-2\sqrt{143}$
• B. $(\sqrt{286})^{24}$
• C. $24$
• D. $1$

Hint:

Expressions of the form $\frac{a}{b} - \frac{b}{a}$ often simplify using $(a^2-b^2)$.

Answer 1

The Correct Option is D