Question

find the values of x and y

Answer 1

For a) Rationalize the denominator i.e. multiply it's conjugate
$= \frac{4 + \sqrt{2} }{2 + \sqrt{2} } \times \frac{2 - \sqrt{2} }{2 - \sqrt{2} }$
$= \frac{8 - 4 \sqrt{2} + 2 \sqrt{2} - 2 }{4 - 2}$
$= \frac{6 - 2 \sqrt{2} }{2} \\ = 3 - \sqrt{2}$
therefore
$x = 3 \: and \: y = 2$

Please apply the same logic for b) also
For c) just cross multiply and subtract you will get the answer


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