Question

3/(√3-√2) = a√3-b√2 . Find the values of a and b.

Answer 1

Hello Mate!

$\frac{3}{ \sqrt{3} - \sqrt{2} } = a \sqrt{3} - b \sqrt{2} \\ \frac{3}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ = \frac{3( \sqrt{3} + \sqrt{2} ) }{3 - 2} = 3 \sqrt{3} + 3 \sqrt{2} \\ 3 \sqrt{3} + 3 \sqrt{2} = a \sqrt{3} - b \sqrt{2 } \\ a = 3 \\ - b = 3 \: or \: b \: = - 3$

Hope it helps☺!✌

Answer 2

Solution:-


$\frac{3}{( \sqrt{3} - \sqrt{2} ) } = a \sqrt{3} - b \sqrt{2} \\ \frac{3}{( \sqrt{3} - \sqrt{2} )} \times \frac{( \sqrt{3} + \sqrt{2}) }{( \sqrt{3} + \sqrt{2}) } \\ \frac{3 \sqrt{3} + 3\sqrt{2} }{3 - 2} \\ 3 \sqrt{3} - 3 \sqrt{2} = a \sqrt{3} - b \sqrt{2} \\ a = 3 \\ b = - 3$