let f:[0;1]→R, prove that ∃x_0 ,x_1 ,x_2 ∈(0;1) such that ((f(x_0 ))/x_0 ^2 )+((f(x_1 ))/(2x_1 ^2 ))=3f(x


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Question Number 140392 by mathdanisur last updated on 07/May/21

$l e t f : [0; 1] \to R, p r o v e t h a t \exists x_{0}, x_{1}, x_{2} \in (0; 1)$ $s u c h t h a t \frac{f (x_{0})}{x_{0}^{2}} + \frac{f (x_{1})}{2 x_{1}^{2}} = 3 f (x_{2})$
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