Question

BRAINLY ALERT
$a = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } b = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$
Find value of
${a}^{2} + {b}^{2}$

Answer 1

$<b >hey here is your answer$

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$a = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \\ = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \: \times \: \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ = \frac{( \sqrt{3} + \sqrt{2} {)}^{2} }{( \sqrt{3} {)}^{2} - ( \sqrt{2} {)}^{2} } \\ \\ = \frac{( \sqrt{3} {)}^{2} + ( \sqrt{2} {)}^{2} + 2 \times \sqrt{3} \times \sqrt{2} }{3 - 2}\\ \\ = \frac{3 + 2 + 2 \sqrt{6} }{1} \\ \\ = 5 + 2 \sqrt{6} \\ \\ \\b = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \\ = \frac{( \sqrt{3} - \sqrt{2} {)}^{2} }{( \sqrt{3} {)}^{2} - ( \sqrt{2} {)}^{2} } \\ \\ = \frac{( \sqrt{3} {)}^{2} + ( \sqrt{2} {)}^{2} - 2 \times \sqrt{3} \times \sqrt{2} }{3 - 2} \\ \\ = \frac{3 + 2 - 2 \sqrt{6} }{1} \\ \\ = 5 - 2 \sqrt{6}$

now ,

${a}^{2} + {b}^{2} = (5 + 2 \sqrt{6} {)}^{2} + (5 - 2 \sqrt{6} {)}^{2} \\ \\ = ( {5})^{2} + (2 \sqrt{6} {)}^{2} + 2 \times 5 \times 2 \sqrt{6} +\\ \\ (5 {)}^{2} + (2 \sqrt{6} {)}^{2} - 2 \times 5 \times 2 \sqrt{6} \\ \\ = 25 + 24 + 20 \sqrt{6} + 25 + 24 - 20 \sqrt{6} \\ \\ = 25 + 24 + 25 + 24 \\ \\ = 98$

98 answer

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hope this helps you

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