Question

find answer for this question

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Answer 1

$x = \frac{ \sqrt{3} + \sqrt{2}}{ \sqrt{3} - \sqrt{2} } \\ \\ \\y =\frac{ \sqrt{3} - \sqrt{2}}{ \sqrt{3} + \sqrt{2} }$

Now we have the following :-

$x + y = \frac{ \sqrt{3} + \sqrt{2}}{ \sqrt{3} - \sqrt{2}} + \frac{ \sqrt{3} - \sqrt{2}}{ \sqrt{3} + \sqrt{2}} \\ \\ \\ \\ = \frac{ {( \sqrt{3} + \sqrt{2})}^{2} + {( \sqrt{3} - \sqrt{2})}^{2} }{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2})} \\ \\ \\ \\ = \frac{3 + 2 + 2 \sqrt{6} + 3 + 2 - 2 \sqrt{6}}{3 - 2} \\ \\ \\ \\ = 10$

Also we have :-

$xy = (\frac{ \sqrt{3} +\sqrt{2}}{ \sqrt{3} -\sqrt{2}})(\frac{ \sqrt{3} - \sqrt{2}}{ \sqrt{3} + \sqrt{2}})\\ \\ \\ \\ = \frac{3 - 2}{3 - 2} \\ \\ \\ = 1$

Now we know that :-

${x}^{2}+{y}^{2} = {(x + y)}^{2} - 2xy \\ \\ \\ \\ = {(10)}^{2} - 2 \\ \\ \\ = 100 - 2 \\ \\ \\ = 98$

Hence,

Answer is 98

Answer 2

let me know if its correct