4MA0 Higher January 2013 Paper 4 Q19
19 \((3 + \sqrt{a})(4 + \sqrt{a}) = 17 + k\sqrt{a}\) where \(a\) and \(k\) are positive integers.
Find the value of \(a\) and the value of \(k\).
(3)
| Scheme | Marks |
|---|---|
\(12 + 3\sqrt{a} + 4\sqrt{a} + a\) or \(12 + 7\sqrt{a} + a\) | M1 |
| \(a = 5\) | A1 |
| \(k = 7\) | B1 |
| (3) |
Notes
M1: Accept \(\sqrt{a}\sqrt{a}\) or \((\sqrt{a})^2\) instead of \(a\)
Award B3 for \(a = 25\), \(k = 11\) or \(a = 1\), \(k = 3\)