Question

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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

HEY MATE !!!

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

so,

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

$= \frac{3 + 2 + 2 \sqrt{6} }{3 + 2 - 2 \sqrt{6} } \\ = \frac{5 + 2 \sqrt{6} }{5 - 2 \sqrt{6} }$

and

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

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

$\frac{3 + 2 - 2 \sqrt{6} }{3 + 2 + 3 \sqrt{6} } \\ \\ \frac{5 - 26}{5 + 2 \sqrt{6} }$

thus,

${x}^{2} - {y}^{2} \\ = \frac{5 + 2 \sqrt{6} }{5 -2 \sqrt{6} } - \frac{5 - 2 \sqrt{6} }{5 + 2 \sqrt{6} }$

$\frac{ ({5 + 2 \sqrt{6} )}^{2} - ({5 - 2 \sqrt{6} )}^{2} }{5 - 2 \sqrt{6} \times 5 + 2 \sqrt{6} }$

$= 40 \sqrt{6} \\ = 40 \times 2.4 \\ = 96$

thus the final answer is 96

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