Question

(a^2+b^2)(b^2+c^2)(c^2+a^2)<8a^2b^2c^2

Answer 1

Explicație pas cu pas:

Incepem de la o inecuatie adevarata:

(a-b)²>=0 => a²-2ab+b²>=0 =>a²+b²>=2ab

Asa facem si cu (b-c)² si (a-c)² si o sa ramanem cu:

a²+b²>=2ab

b²+c²>=2bc

a²+c²>=2ac

Deci (a²+b²)(b²+c²)(a²+c²)>=2ab×2bc×2ac =>(a²+b²)(b²+c²)(a²+c²)>=8a²b²c²