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

The roots of the equation are $$(a +\sqrt b)$$ and $$(a -\sqrt b)$$​​

For a quadratic equation with roots r_1 and r_2​, the standard form is:

​$$x^2 - (\text{Sum of roots})x + (\text{Product of roots}) = 0$$​​

Sum of roots = $$r_1 + r_2$$, Product of roots = $$r_1 \cdot r_2$$​ 

Sum of roots = (a + b) + (a - b) = 2a

Product of roots = $$(a +\sqrt b)(a -\sqrt b)= a^2-b$$​  

Substituting the sum and product into the quadratic form:

​$$x^2 - (\text{Sum of roots})x + (\text{Product of roots}) = 0 \\ \ \\ \bf x^2 -2ax + (a^2 -b) = 0$$​​