Inegalitate in doua variabile pozitive

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alex2008
Leibniz
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Inegalitate in doua variabile pozitive

Post by alex2008 »

Fie \( a,b>0 \) . Sa se demonstreze ca :

\(
\left(a^2+b+\frac{3}{4}\right)\left(b^2+a+\frac{3}{4}\right)\ge \left(2a+\frac{1}{2}\right)\left(2b+\frac{1}{2}\right) \)
. 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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Post by Marius Mainea »

Aplicam AM-GM

\( LHS\ge (a+b+\frac{1}{2})^2\ge 4(a+\frac{1}{4})(b+\frac{1}{4})=RHS \)
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