Question

find the values of a and b in each of the following 5 -√6 / 5+√6 = a -b √6​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

To prove -

$\frac{5 - \sqrt{6}}{5 + \sqrt{6} } = a - b \sqrt{6}$

Explanation -

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

Hence this cannot be written in the form of a-b√6.