Higher January 2021 Paper 1 Q18
18 Given that \((8 - \sqrt{x})(5 + \sqrt{x}) = y\sqrt{x} + 21\) where \(x\) is a prime number and \(y\) is an integer,
find the value of \(x\) and the value of \(y\).
Show each stage of your working clearly.
(3)
| Scheme | Marks |
|---|---|
e.g. \(40 + 8\sqrt{x} - 5\sqrt{x} - \sqrt{x}\sqrt{x}\) or \(40 + 8\sqrt{x} - 5\sqrt{x} - \left(\sqrt{x}\right)^2\) or \(40 + 8\sqrt{x} - 5\sqrt{x} - x\) or \(40 + 3\sqrt{x} - x\) | M1 |
| Working required Answer: \(x = 19\) | A1 |
| \(y = 3\) | B1 |
| (3) | |
| (3 marks) |
Notes
M1: for a correct expansion with at least 3 out of 4 terms correct oe or all 3 terms correct
A1: (dep on M1) for \(x = 19\)
B1: for \(y = 3\)