Find the value of \(a\)
If \[ \sqrt{13 – a\sqrt{10}} = \sqrt{8} + \sqrt{5} \]
(a) −5 \quad (b) −6 \quad (c) −4 \quad (d) −2
Solution:
\[ \sqrt{8} = 2\sqrt{2} \Rightarrow \sqrt{8} + \sqrt{5} = 2\sqrt{2} + \sqrt{5} \]
\[ (2\sqrt{2} + \sqrt{5})^2 = 8 + 5 + 4\sqrt{10} = 13 + 4\sqrt{10} \]
\[ 13 – a\sqrt{10} = 13 + 4\sqrt{10} \]
\[ -a = 4 \Rightarrow a = -4 \]
\[ \therefore \text{Correct Answer: } -4 \ (\text{Option c}) \]