If `x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))` and `y=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))`, then find the value of `x^2+y^2`.

Explanation

`x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}`


Rationalising the denominator, we get


`x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}} \times \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}} `


`\Rightarrow x=\frac{3+2+2 \sqrt{6}}{3-2} `

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