If x = √3+√2/√3-√2 and y = √3-√2/√3+√2, then find the value of x^2 + y^2.

Question

If x = \(\frac {\sqrt3 + \sqrt2}{\sqrt3 - \sqrt2}\) and y = \(\frac {\sqrt3 - \sqrt2}{\sqrt3 + \sqrt2}\), then find the value of x² + y².

x = √3+√2/√3-√2 and y = √3-√2/√3+√2

Answer 1

Given that x = \(\frac {\sqrt3 + \sqrt2}{\sqrt3 - \sqrt2}\) 

R.F. of √3 – √2 is √3 + √2

x² + y² = (5 + 2√6 )² + (5 – 2√6 )² 

= 25 + 20√6 + 24 + 25 – 20√6 + 24 

= 98