Question

Find the value of a and b if
$3 - \sqrt{5} \div3 + 2 \sqrt{5} = a \sqrt{5} - b$

Answer 1

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Answer 2

ANS.

$\frac{3 - \sqrt{5} }{3 + 2 \sqrt{5} } \\ = \frac{(3 - \sqrt{5})(3 - 2 \sqrt{5}) }{(3 + 2\sqrt{5} )(3 - 2 \sqrt{5}) } \\ = \frac{9 - 6 \sqrt{5} - 3 \sqrt{5} + 10}{9 - 20} \\ = \frac{19 - 9 \sqrt{5} }{ - 11} \\ = ( - \frac{19}{11} ) + ( \frac{9}{11} ) \sqrt{5} \\ = - b + a \sqrt{5} \: \: \: (given)\\ \\ \\ so \\ a = \frac{9}{11} \: \: \: and \: \: \: b = \frac{19}{11}$

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