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Inegalitate
Posted: Sun Jan 25, 2009 3:07 pm
by alex2008
Aratati ca :
\( a^2+b^2+c^2+d^2+e^2\ge a(b+c+d+e) , (\forall)a,b,c,d,e \in \mathbb{R} \)
Posted: Sun Jan 25, 2009 4:29 pm
by Marius Mainea
\( LHS\ge a^2+\frac{(b+c+d+e)^^2}{4}\ge a(b+c+d+e) \)
Posted: Sun Jan 25, 2009 4:40 pm
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 \( x^2+y^2\ge 2xy \)