Question

If x = √3 + √2/√3 - √2then find the value of x2

Answer 1

Answer:

$x = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \\ {x}^{2} = {(\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} })}^{2} \\ \\ = \frac{ { (\sqrt{3} - \sqrt{2} }^{2}) }{( { \sqrt{3} + \sqrt{2} }^{2}) } \\ \\ = \frac{3 - 2 \sqrt{6} + 2 }{3 + 2 \sqrt{6} + 2 } \\ \\ = \frac{5 - 2 \sqrt{6} }{5 + 2 \sqrt{6} }$