Question 91
Let $a, b, c$ be distinct positive real numbers. Prove that the equation
$$
(a+b+c) x^{2}+2\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right) x+\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=0
$$
has two distinct real solutions.
$$
(a+b+c) x^{2}+2\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right) x+\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=0
$$
has two distinct real solutions.