Inegalitate 5

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Marius Mainea
Gauss
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Inegalitate 5

Post by Marius Mainea »

Daca a,b,c sunt pozitive atunci

\( \frac{(a+b)^2}{c}+\frac{c^2}{a}\ge 4b \)

T. Andreescu M.R.
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alex2008
Leibniz
Posts: 464
Joined: Sun Oct 19, 2008 3:23 pm
Location: Tulcea

Post by alex2008 »

Din Titu Andreescu avem ca :

\( LHS\ge \frac{(a+b+c)^2}{c+a} \) si e suficient sa aratam ca \( \frac{(a+b+c)^2}{c+a}\ge 4b \Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ca\ge 4ab+4bc \Leftrightarrow (a-b+c)^2\ge 0 \)
. A snake that slithers on the ground can only dream of flying through the air.
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