Find the equation whose roots are $$(a+\sqrt{b})$$ and $$(a-\sqrt{b})$$

By option C,

$$x^2 - 2ax + (a^2-b) = 0$$

$$\Rightarrow x^2 - \left(a\ +\ \sqrt{\ b}\right)x\ -\ \left(a\ -\ \sqrt{\ b}\right)x + (a^2-b) = 0$$

$$\Rightarrow x\left(x\ -\ \left(a\ +\ \sqrt{\ b}\right)\right)\ -\ \left(a\ -\ \sqrt{\ b}\right)\left(x\ -\ \left(a\ +\ \sqrt{\ b}\right)\right) = 0$$

$$\Rightarrow \left(x\ -\ \ \left(a+\ \sqrt{\ b}\right)\right)\left(x\ -\ \left(a+\ \sqrt{\ b}\right)\right) = 0$$

$$\Rightarrow x = \left(a\ +\ \sqrt{\ b}\right)$$ or $$x = \left(a\ -\ \sqrt{\ b}\right)$$