Question

5 + root 6 divided by 5 minus root 6 is equal to a + b root 6 wrestlers the denominator

Answer 1

Here is ur answer
Hope u understood when i divided the values of a and b with corresponding values...

Answer 2

Answer:

$a=\frac{31}{19}\:\:and\;\:b=\frac{10}{19}$

Step-by-step explanation:

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

To find: Value of a & b

We rationalize the denominator of LHS

Consider,

LHS

$\implies\frac{5+\sqrt{6}}{5-\sqrt{6}}$

$\implies\frac{5+\sqrt{6}}{5-\sqrt{6}}\times\frac{5+\sqrt{6}}{5+\sqrt{6}}$

$\implies\frac{(5+\sqrt{6})^2}{5^2-(\sqrt{6})^2}$

$\implies\frac{25+6+2\times5\sqrt{6}}{25-6}$

$\implies\frac{31+10\sqrt{6}}{19}$

$\implies\frac{31}{19}+\frac{10\sqrt{6}}{19}$

Now by comparing with RHS, we get

$a=\frac{31}{19}\:\:and\;\:b=\frac{10}{19}$

Therefore,   $a=\frac{31}{19}\:\:and\;\:b=\frac{10}{19}$