(a) Express $\frac{6\sqrt{2}-9}{\sqrt{2}-1}$in the form of $a+b\sqrt{2}$, where $a$ and \

Question

(a) Express $\frac{6\sqrt{2}-9}{\sqrt{2}-1}$in the form of $a+b\sqrt{2}$, where $a$ and $b$ are integers.[2] (b) $\frac{6\sqrt{2}-9}{\sqrt{2}-1}$ is a root of the equation $x^2 + px + q = 0$ where $p$ and $q$ are integers. Using the result in part (a), find the value of $p$ and of $q$.[4]

Accepted Answer

(a)a=3, b=-3 (b)p=-6, q=-9

2025 CGSS PRELIMS P1 Q1

2025 CGSS PRELIMS P1 Q1