Question

If
$\frac{3 + \sqrt{2} }{3 - \sqrt{2} }$
=a+b×
$\sqrt{2}$
, find the values of a and b.

With Full Workings.
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Answer 1

Answer:

The answer is

$a = \frac{11}{7} \\ b = \frac{6}{7}$

Step-by-step explanation:

$\frac{3 + \sqrt{2} }{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } \\ = \frac{9 + 3 \sqrt{2} + 3 \sqrt{2} + 2}{9 - 3 \sqrt{2} + 3 \sqrt{2} - 2 } \\ = \frac{11 + 6 \sqrt{2} }{7} \\ = \frac{11}{7} + \frac{6}{7} \sqrt{2}$

In comparison

Then

$a = \frac{11}{7} \\ b = \frac{6}{7}$