Find the value of \(x\)
\[ \sqrt{13 – x\sqrt{10}} = \sqrt{8} + \sqrt{5} \]
Solution:
\[ \sqrt{8} = 2\sqrt{2} \Rightarrow \sqrt{8} + \sqrt{5} = 2\sqrt{2} + \sqrt{5} \]
\[ (\,2\sqrt{2} + \sqrt{5}\,)^2 = 13 – x\sqrt{10} \]
\[ = 8 + 5 + 4\sqrt{10} = 13 + 4\sqrt{10} \]
\[ 13 + 4\sqrt{10} = 13 – x\sqrt{10} \]
\[ 4\sqrt{10} = -x\sqrt{10} \Rightarrow x = -4 \]