# Mutually tangent line

Calculus Level 4

A straight line is drawn in a plane such that it is tangent to both curves $$y=\sqrt {x}$$ and $$y=-\frac {1} {x}$$. If the area of the region bound by this line, the $$x$$-axis and the curve $$y=\sqrt {x}$$ is equal to $$\frac {a} {b}$$ where $$a$$ and $$b$$ are coprime positive integers, find the value of $$a+b$$.

×