Question

5-✔6 upon 5+✔6 = a-b✔6 . find the value of a and b ​

Answer 1

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Answer 2

$\frac{5 - \sqrt{6} }{5 + \sqrt{6} } = a - b \sqrt{6} \\ \frac{5 - \sqrt{6} }{5 + \sqrt{6} } \times \frac{5 - \sqrt{6} }{5 - \sqrt{6} } = a - b \sqrt{6} \\ \frac{( {5})^{2} + ( \sqrt{6} ) ^{2} - 2(5) ( \sqrt{6} )}{ ({5})^{2} - ( \sqrt{6} ) ^{2} } = a - b \sqrt{6} \\ \frac{25 + 6 - 10 \sqrt{6} }{25 - 6} = a - b \sqrt{6} \\ \frac{31 - 10 \sqrt{6} }{ 19} = a - b \sqrt{6} \\ a = \frac{31}{19} \: \: \: \: \: and \: \: \: b = \frac{10}{19}$