Question 147
Let $ABC$ be a triangle with $m(\angle A)\gt 90^{\circ}$ and let $a=|BC|$, $b=|AC|$, $c=|AB|$ be its side lengths. Prove that the equation
$$
x^{2}-(a+b+c)x+b^{2}+c^{2}=0
$$
has two distinct real solutions.
$$
x^{2}-(a+b+c)x+b^{2}+c^{2}=0
$$
has two distinct real solutions.