Question

Find the values of A and B in each of the following 2 + under root 3 upon 2 minus under root 3 is equals to a + b under root 3

Answer 1

Step-by-step explanation:

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } = a + b \sqrt{3} \\ \frac{4 + 3 + 4 \sqrt{3} }{4 - 3} = a + b \sqrt{3} \\ 7 + 4\sqrt{3} = a + b \sqrt{3} \\ a = 7 \: and \: b = 4$

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