Inegalitate

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alex2008
Leibniz
Posts: 464
Joined: Sun Oct 19, 2008 3:23 pm
Location: Tulcea

Inegalitate

Post by alex2008 »

Aratati ca :
\( a^2+b^2+c^2+d^2+e^2\ge a(b+c+d+e) , (\forall)a,b,c,d,e \in \mathbb{R} \)
. A snake that slithers on the ground can only dream of flying through the air.
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Marius Mainea
Gauss
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Location: Gaesti (Dambovita)

Post by Marius Mainea »

\( LHS\ge a^2+\frac{(b+c+d+e)^^2}{4}\ge a(b+c+d+e) \)
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alex2008
Leibniz
Posts: 464
Joined: Sun Oct 19, 2008 3:23 pm
Location: Tulcea

Post by alex2008 »

Sau \( LHS=a^2+b^2+c^2+d^2+e^2=\frac{a^2}{4}+b^2+\frac{a^2}{4}+c^2+\frac{a^2}{4}+d^2+\frac{a^2}{4}+e^2\ge ab+ac+ad+ae \) , unde am folosit \( x^2+y^2\ge 2xy \)
. A snake that slithers on the ground can only dream of flying through the air.
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