C1 2015 1 Edexcel

1

(a)

We have:

(2 \sqrt 5) = 2^2 (\sqrt 5)^2 = 4 \times 5 = 20

(b)

Rationalising the denominator we have:

\begin{align*}\frac {\sqrt 2} {2 \sqrt 5 - 3 \sqrt 2} & = \frac {\sqrt 2(2 \sqrt 5 + 3 \sqrt 2)} {(2 \sqrt 5 + 3 \sqrt 2)(2 \sqrt 5 - 3 \sqrt 2)} \\ & = \frac {2 \sqrt {10} +3 (\sqrt 2)^2} {(2 \sqrt 5)^2 - (3 \sqrt 2)^2} \\ & = \frac {2 \sqrt {10} + 6} {20 - 18} \\ & = \frac {2 \sqrt{10} + 6} 2 \\ & = 3 + \sqrt{10}\end{align*}

So a = 3, b = 10.

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