Question

if a =√3+√2/√3-√2and b=√3-√2/√3+√2 then find a²+b² answer in detail​

Answer 1

$a = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \\ b = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ a + b = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } + \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ = \frac{( { \sqrt{3} + \sqrt{2} })^{2} + ( { \sqrt{3} - \sqrt{2} })^{2} }{3 - 2} \\ = 3 + 2 + 3 + 2 \\ = 10 \\ \\ ab = 1 \\ \\ {a}^{2} + {b}^{2} = ( {a + b})^{2} - 2ab \\ = {10}^{2} - 2 \times 1 \\ = 100 - 2 \\ = 98$