Question

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

Answer 1

Answer: 98

Given following:

$\Longrightarrow \sf x = \dfrac{\sqrt{3} +\sqrt{2} }{\sqrt{3} - \sqrt{2} }$

$\Longrightarrow \sf y = \dfrac{\sqrt{3} -\sqrt{2} }{\sqrt{3} + \sqrt{2} }$

Solve for x² + y²:

$\rightarrow \sf \left(\:\dfrac{\sqrt{3}\:+\sqrt{2}\:\:}{\sqrt{3}\:-\:\sqrt{2}\:}\right)^2\:+\:\left(\dfrac{\sqrt{3}\:\:-\sqrt{2}\:\:}{\sqrt{3}\:+\:\sqrt{2}\:\:}\:\right)^2$

simplify following

$\rightarrow \sf 49+20\sqrt{6}+49-20\sqrt{6}$

add/subtract similar terms

$\rightarrow \sf 98$