Question

If x=$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and y = $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, then x² + y +y² =

(a) 101
(b) 99
(c) 98
(d) 102

Answer 1

Given that and.

We need to find

Now we will rationalize x. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Similarly, we can rationalize y. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get

Therefore,

Hence the value of the given expression is.