A series of equations

Question

ax+y-2=0 x-ay+3=0 2x+y-a=0

Find a if (a,a) lies inside the triangle formed by these three lines

Answer 1

Assuming $a,b \in\mathbb{R}$, you have

$$ a^2+2ab+4b^2 = a^2+2ab+b^2+3b^2 = (a+b)^2 +3b^2 \geq 0.$$