Question

if x= √3+√2/√3-√2 and y=√3-√2/√3+√2 then find the value of x² + y²​

Answer 1

$x = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ y = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ x + y = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } + \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{ 3} + \sqrt{2} } \\ = \frac{( { \sqrt{3} + \sqrt{2} })^{2} + ( { \sqrt{3} - \sqrt{2} })^{2} }{3 - 2} \\ = 2(( { \sqrt{3} })^{2} + ( { \sqrt{2} })^{2} ) \\ = 2(3 + 2) \\ = 10 \\ xy = 1 \\ {x}^{2} + {y}^{2} = ( {x + y})^{2} - 2xy \\ = ( {10})^{2} - 2 \times 1 \\ = 100 - 2 \\ = 98$

Answer 2

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