Question

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

Answer 1

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`