Winter Holiday Homework: Radical Expressions #2

$a = \frac{1}{\sqrt{3} - \sqrt{2}}, b = \frac{1}{\sqrt{3} + \sqrt{2}}$ $\Rightarrow a ={\sqrt{3} + \sqrt{2}}, b = {\sqrt{3} - \sqrt{2}}$

$\boxed{ {\left(x + y\right)}^2 + {\left(x - y\right)}^2 = 2{x}^2 + 2{y}^2}$ $\Rightarrow a^2 + b^2 = 10$

$\boxed{ {\left(x + y\right)\left(x - y\right) } = x^2 - y^2 }$ $\Rightarrow -3ab = -3$

$\Rightarrow a^2 - 3ab + b^2 = \boxed7$