Existence Problem for Functional Equation on (0,1)

Να αποδείξετε ότι υπάρχουν αριθμοί \(x_1, x_2, x_3 \in (0,1)\) τέτοιοι ώστε \[ \frac{f(x_1)}{4x_1} + \frac{f(x_2)}{6x_2^{2}} = f(x_3). \]

Prove that there exist numbers \(x_1, x_2, x_3 \in (0,1)\) such that \[ \frac{f(x_1)}{4x_1} + \frac{f(x_2)}{6x_2^{2}} = f(x_3). \]