Question

please solve this question

Answer 1

Solution:

First rationalise denominator of both x and y

$x = \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\ = \frac{( { \sqrt{5} - \sqrt{3} })^{2} }{5 - 3} \\ \\ x = \frac{5 + 3 - 2 \sqrt{15} }{2} \\ \\ x = 4 - \sqrt{15}$
by the same way

$y =4 + \sqrt{15}$
now put these values in the eq

${x}^{2} + {y}^{2} - 6xy \\ \\ ( {4 - \sqrt{15} })^{2} + {(4 + \sqrt{15}) }^{2} - 6(4 - \sqrt{15} )(4 + \sqrt{15} ) \\ \\ 16 + 15 - 8 \sqrt{15} + 16 + 15 + 8 \sqrt{15} - 6(16 - 15) \\ \\ = 31 + 31 - 6 \\ \\ = 62 - 6 \\ \\ = 56$
hope it helps you