4MA0 Higher June 2013 Paper 3R Q22
22 \(\left(\sqrt{a} + \sqrt{8a}\right)^2 = 54 + b\sqrt{2}\)
\(a\) and \(b\) are positive integers.
Find the value of \(a\) and the value of \(b\).
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
| \((\sqrt{a})^2 + (\sqrt{8a})^2 + 2\sqrt{a}\sqrt{8a}\) | M1 |
\(a + 8a + 2a\sqrt{8}\) \(9a + 4a\sqrt{2}\) | A1 |
| \(a = 6\) \(b = 24\) | A1 |
| (3) |
Notes
M1: for correct expansion of brackets
A1: for \(9a + 4a\sqrt{2}\)