# Finding UnKnown By Comparing Equation with Surd

## 2014 Oct Nov Paper 21 & 22 Q9

Integers $$a$$ and $$b$$ are such that $$(a+3 \sqrt{5})^{2}+a-b \sqrt{5}=51$$. Find the possible values of $$a$$ and the corresponding values of $$b$$.

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## 2016 Oct Nov Paper 21 & 22 Q2

Without using a calculator, find the integers $$a$$ and $$b$$ such that $$\frac{a}{\sqrt{3}+1}+\frac{b}{\sqrt{3}-1}=\sqrt{3}-3$$.

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## 2016 May June Paper 21 & 23

Do not use a calculator in this question.
(b) Given that $$28+p \sqrt{3}=(q+2 \sqrt{3})^{2}$$, where $$p$$ and $$q$$ are integers, find the values of $$p$$ and of $$q$$.

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