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

Question

Express $\frac{6\sqrt{2}-9}{\sqrt{2}-1}$in the form of $a+b\sqrt{2}$, where $a$ and $b$ are integers.[2] $\frac{6\sqrt{2}-9}{\sqrt{2}-1}$ 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

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