Question

If $(a,a^2)$ falls inside the angle the angle made by lines $y=\frac{x}{2},x>0$ and $y=3x,x>0,$ , then a belongs to:

Answer 1

Consider the given lines are

$y=\frac{x}{2}(x>0)$ and $y=3x(x>0)$

Given points $(a^2,a)$ be the lies both lines and we get,

$a^2-\frac{a}{2}>0......\left(1\right)$ and $a^2-3a<0......\left(2\right)$

By solve equation (1) and (2) to,

$\frac{1}{2}<a<3$

Hence it is complete solution.