Inegalitate in trei variable nenegative
Posted: Mon May 04, 2009 10:49 am
Fie \( x,y,z\ge 0 \) . Sa se arate ca :
\( x(x-z)^2+y(y-z)^2\ge (x-z)(y-z)(x+y-z) \)
\( x(x-z)^2+y(y-z)^2\ge (x-z)(y-z)(x+y-z) \)
Desfacand paranteze inegalitatea se reduce la
\( \sum_{cyc} x^3+3xyz\ge \sum_{sym} x^2y \) care este evidenta.