Question

$$\frac{ 8 }{ \sqrt{ 3+ \sqrt{ 5 } } } = \frac{ 8 \times ( \sqrt{ 3- \sqrt{ 5) } } }{ ( \sqrt{ 3+ \sqrt{ 5) } } ( \sqrt{ 3- \sqrt{ 5) } } }$$

Answer

[Infinite Solutions]

Solution


Remove parentheses.
\[\frac{8}{\sqrt{3+\sqrt{5}}}=\frac{8\sqrt{3-\sqrt{5}}}{\sqrt{3+\sqrt{5}}\sqrt{3-\sqrt{5}}}\]
Since both sides equal, there are infinitely many solutions.
Infinitely Many Solutions