If x, y are rational numbers and $$\frac{5+\sqrt{11}}{3-2\sqrt{11}}$$= x + y$$\ \sqrt{11}$$. The values of x and y are

$$\frac{5+\sqrt{11}}{3-2\sqrt{11}} = x+y\sqrt{11}$$

Rationalising above equation

$$\frac{5+\sqrt{11}}{3-2\sqrt{11}}\times \frac{3+2\sqrt{11}}{3+2\sqrt{11}} = x+y\sqrt{11}$$

$$\Rightarrow \frac{15+10\sqrt{11}+3\sqrt{11}+22}{9-44} = x+y\sqrt{11}$$

$$\Rightarrow \frac{37+13\sqrt{11}}{-35} = x+y\sqrt{11}$$

 $$\Rightarrow$$ ($$\frac{-37}{35})$$+($$\frac{-13}{35}$$)$$\sqrt{11} =$$ $$x+y\sqrt{11}$$

Comparing above equations

x $$= \frac{-37}{35}$$ and y $$= \frac{-13}{35}$$