Question

if x=√3+√2/√3-√2 and y=√3-√2/√3+√2 then find x^2+y^2-5xy​

Answer 1

${ (\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } )}^{2} + {( \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} }) }^{2} - 5( \frac{\sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2}})({\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} }) } \\ \\ = \frac{5 + 2 \sqrt{6} }{5 - 2 \sqrt{6} } + \frac{5 - 2 \sqrt{6} }{5 + 2 \sqrt{6} } - 5 \\ \\ = \frac{ ({5 + 2 \sqrt{6} ) }^{2} + ( {5 - 2 \sqrt{6} })^{2} }{25 - 24} - 5 \\ \\ = \frac{25 + 24 + 25 \sqrt{6} + 25 + 24 - 20 \sqrt{6} }{1} - 5 \\ \\ = 98 - 5 \\ \\ = 93$