Question

pls help its urgent i need it

Answer 1

$\huge\mathfrak\red{question}$

$if \: \: x \: = \frac{ \sqrt{6} + \sqrt{7} }{ \sqrt{7} - \sqrt{6} } \: y = \frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} + \sqrt{6} } find \: x^{2} + {y}^{2}$

$\huge\mathfrak\blue{ Solution}$

$\bf \: {consider \: \: \: \: \: x }$

$x = \frac{ \sqrt{6} + \sqrt{7} }{ \sqrt{7} - \sqrt{6} }$

$x = \frac{ ( \sqrt{6} + \sqrt{7} )^{2} }{ (\sqrt{7} - \sqrt{6}) \times ( \sqrt{7} + \sqrt{6} ) }$

$x = \frac{13+ 2 \sqrt{42} }{7 - 6}$

$x = 13 + 2 \sqrt{42}$

$\bf{consider \: \: \: \: \: y \: }$

$y = \frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} + \sqrt{6} }$

$y = \frac{( \sqrt{7} - \sqrt{6}) ^{2} }{ \sqrt{7} ^{2} - \sqrt{6}^{2} }$

$y = 13- 2 \sqrt{42}$

${x}^{2} + {y}^{2} = (13 + 2 \sqrt{42}) ^{2} + (13 - 2 \sqrt{42} )^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2(13 ^{2} +( 2 \sqrt{42} )^{2} )$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2(169 + 168)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: = 674$