Produs de expresii, own

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Filip Chindea
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Joined: Thu Sep 27, 2007 9:01 pm
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Produs de expresii, own

Post by Filip Chindea »

Pentru numerele reale \( u, v, w > 0 \) si \( r \) definim

\( F_r(u, v, w) \ := (u - v)(u + w)^r + (u - w)(u + v)^r \).

Demonstrati ca pentru orice \( a, b, c > 0 \) si \( r \in \mathbb{R} \),

\( \sum \frac{F_r(b, c, a) \cdot F_r(c, a, b)}{(b + c)^{r-2}} \le 0 \).
Life is complex: it has real and imaginary components.
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