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Question

Find the value of 'a' in the following equation:
$\frac{2 + \sqrt{3}}{2 - \sqrt{3}} = a + b \sqrt{3}$

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Solution

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We rationalize the denominator,
$∴ \frac{2 + \sqrt{3}}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}}$
$= \frac{4 + 3 + 4 \sqrt{3}}{4 - 3}$
$= 7 + 4 \sqrt{3}$
$⟹ a = 7, b = 4$

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