# How do you solve sqrt(k+9)-sqrtk=sqrt3?

May 14, 2017

$k = 3$

#### Explanation:

The feasibility conditions are

$k + 9 \ge 0$ and $k \ge 0$ so $\Rightarrow k \ge 0$

so by inspection, the solution is for $k = 3$ because then

$\sqrt{3 + 9} - \sqrt{3} = \sqrt{3}$ or

$\sqrt{4 \times 3} = 2 \sqrt{3} = \sqrt{3} + \sqrt{3}$