If $$\frac{\sqrt5+\sqrt2}{\sqrt5-\sqrt2}$$​ = a + b$$\sqrt{10}$$​, then which of the following is correct?

Correct option is D

Given:

​$$\frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} - \sqrt{2}} = a + b\sqrt{10}$$

Formula Used:​

( a + b )² = a² + b² + 2ab

a² - b² = ( a - b ) ( a + b ) 

Solution:

$$\frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} - \sqrt{2}} \cdot \frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}} = a + b\sqrt{10}$$​

​$$​\frac{(\sqrt{5} + \sqrt{2})^2}{(\sqrt{5})^2 - (\sqrt{2})^2} = a + b\sqrt{10}$$​​

​$$\frac{7 + 2\sqrt{10}}{3} = a + b\sqrt{10}$$​​

So,

​$$a = \frac{7}{3}, \quad b = \frac{2}{3}$$​