Question 167
Let $a, b, c$ be positive real numbers, $a \leq b, a \leq c$, such that
$$
\frac{a^{2}+b^{2}+c^{2}}{a(b+c)}=\frac{3}{2}.
$$
Prove that $a=b=c$.
$$
\frac{a^{2}+b^{2}+c^{2}}{a(b+c)}=\frac{3}{2}.
$$
Prove that $a=b=c$.
MathNet 2017-part-03 — 176 problems (EN–VI) Question 167
Math Olympiad Vault · MathNet 2017-part-03 — 176 problems (EN–VI)