Question

please solve fast
anyone solving I will mark brainly​

Answer 1

To find :

the value of a and b

Given :

$\frac{6}{2 \sqrt{7} - 5} = a \sqrt{7} + b$

Solution :

First we need to find the Rationalising Factor (RF) of the term :

$\frac{6}{2 \sqrt{7} - 5}$

so, RF in the form of :

(a-b)(a+b) = a²-b²

so, RF of the term :

$\frac{6}{2 \sqrt{7} - 5} \times \frac{2 \sqrt{7} + 5}{2 \sqrt{7} + 5} \\ \\ = \frac{6(2 \sqrt{7} + 5) }{ ( { 2\sqrt{7} })^{2} - {5}^{2} } \\ \\ = \frac{12 \sqrt{7} + 30}{14 - 25} \\ \\ = \frac{12 \sqrt{7} + 30}{ - 11} \\ \\ = \frac{12 \sqrt{7} }{ - 11} + \frac{30}{ - 11}$

hence,

$\frac{6}{2 \sqrt{7} - 5 } = \frac{12 \sqrt{7} }{ - 11} + \frac{30}{ - 11}$

so, as Given,

$\frac{6}{2 \sqrt{7} - 5} = a \sqrt{7} + b \\ so \: \frac{12 \sqrt{7} }{ - 11} + \frac{30}{ - 11} = a \sqrt{7} + b \\ = > a = \frac{12 \sqrt{7} }{ - 11} and</strong><strong>\:b = \frac{30}{ - 11}$