Question

Please find the value of a and b 2+root3 divided by 2-root3 = a + broot 3

Answer 1

SOLUTION :

$given \: \frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ \\ \: rationalizating \: the \: denominator \\ \\ = > \frac{(2 + \sqrt{3})(2 + \sqrt{3}) }{(2 - \sqrt{3})(2 + \sqrt{3}) } = a + b \sqrt{3} \\ \\ = > \frac{(2 + \sqrt{3}) {}^{2} }{4 - 3} = a + b \sqrt{3} \\ \\ = > \frac{4 + 3 + 4 \sqrt{3} }{1} = a + b \sqrt{3} \\ \\ = > 7 + 4 \sqrt{3} = a + b \sqrt{3} \\ \\ by \: comparing \: on \: both \: sides \: \\ \\ a = 7 \: \: and \: \: b = 4$

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