Question

2 root 6- root 5 / 3 root 5 - 2 root 6 = a + b root 30

Answer 1

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Answer 2

Answer:

$a=\frac{3}{7}\text{ and }b=\frac{4}{21}$

Step-by-step explanation:

The equation is given to be :

$\frac{2\sqrt 6-\sqrt 5}{3\sqrt 5-2\sqrt 6}=a+b\sqrt{30}$

We need to find the value of a and b

$\implies \frac{2\sqrt 6-\sqrt 5}{3\sqrt 5-2\sqrt 6}\\\\\implies \frac{2\sqrt 6-\sqrt 5}{3\sqrt 5-2\sqrt 6}\times \frac{3\sqrt 5+2\sqrt 6}{3\sqrt 5+2\sqrt 6}\\\\\implies \frac{( 2\sqrt 6-\sqrt 5)(3\sqrt 5+2\sqrt 6)}{(3\sqrt 5-2\sqrt 6)(3\sqrt 5+2\sqrt 6)}\\\\\implies \frac{6\sqrt{30}+24-15-2\sqrt{30}}{9\times 5-4\times 6}\\\\\implies \frac{9+4\sqrt{30}}{45-24}\\\\\implies\frac{9}{21}+\frac{4\sqrt{30}}{21}\\\\\implies \frac{3}{7}+\frac{4\sqrt{30}}{21}$

$\text{Now, Comparing it with }a+b\sqrt{30}$

$a=\frac{3}{7}\text{ and }b=\frac{4}{21}$