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X = √3 + √2/ √3 - √2
y = √3 - √2/ √3 + √2
Find x² + y²

1 Answer

5 votes

Answer: 98

Given following:


\Longrightarrow \sf x = (√(3) +√(2) )/(√(3) - √(2) )


\Longrightarrow \sf y = (√(3) -√(2) )/(√(3) + √(2) )

Solve for x² + y²:


\rightarrow \sf \left(\:(√(3)\:+√(2)\:\:)/(√(3)\:-\:√(2)\:)\right)^2\:+\:\left((√(3)\:\:-√(2)\:\:)/(√(3)\:+\:√(2)\:\:)\:\right)^2

simplify following


\rightarrow \sf 49+20√(6)+49-20√(6)

add/subtract similar terms


\rightarrow \sf 98

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