Inegalitate interesanta in triunghi
Posted: Sun May 11, 2008 2:06 pm
Sa se arate ca in orice triunghi ABC are loc inegalitatea:
\( 2(a^2+b^2+c^2)^3+2(a^3b^3+b^3c^3+c^3a^3)+abc(a^3+b^3+c^3)+18a^2b^2c^2\ge 9(a^2+b^2+c^2)(a^2b^2+b^2c^2+c^2a^2) \)
\( 2(a^2+b^2+c^2)^3+2(a^3b^3+b^3c^3+c^3a^3)+abc(a^3+b^3+c^3)+18a^2b^2c^2\ge 9(a^2+b^2+c^2)(a^2b^2+b^2c^2+c^2a^2) \)