Question

x=√3 + √2 / √3 -√2
y=√3-√2 / √3 + √2
Find x^2 + xy -y ^2

Answer 1

X= (√3+√2)/(√3+√2)

=(√3-√2)^2/(√3^2 - √2^2)

=(3-2√6+2) / 1

=5 - 2√6

Similarly,

Y=5+2√6

Therefore, X+Y= 5-2√6+5+2√6

=10

And, XY= (5-2√6) (5+2√6)

=5^2 - (2√6)^2

=25-24

=1

Now,

X^2 + Y^2 + XY

= X^2 + Y^2 + 2XY - XY

=(X+Y)^2 - XY

=(10)^2 - 1

= 100-1

=99

answers is 99