Question

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

Answer 1

I know my writing is very bad.
but I hope it will help you

Answer 2

x = √3 + √2  =  (√3 + √2) (√3 + √2)  =    (√3 + √2)²  = 3 + 2 + 2√6 = 5 + 2√6

      √3 - √2         (√3 - √2) (√3 + √2)         (√3)² - (√2)²

x² = (5 + 2√6)² = 25 + 24 + 20√6 = 49 + 20√6

y =    √3 - √2    =  (√3 - √2) (√3 - √2) =  (√3 - √2)² = 3 + 2 - 2√6 = 5 - 2√6

       √3 + √2         (√3 + √2) (√3 - √2)     (√3)² - (√2)²

y² = (5 - 2√6)² = 25 + 24 - 20√6 = 49 - 20√6

xy = (5 + 2√6) (5 - 2√6) = 25 - 24 = 1

x² + xy - y² = 49 + 20√6 + 1 - 49 + 20√6 = 1 + 40√6