Ta có :P=ab(b−c)(c−a)+bc(c−a)(a−b)+ca(a−b)(b−c)=ab(a−b)+bc(b−c)+ca(c−a)(a−b)(b−c)(c−a)=ab(a−b)−bc(a−b+c−a)+ca(c−a)(a−b)(b−c)(c−a)=(a−b)(ab−bc)+(c−a)(ca−bc)(a−b)(b−c)(c−a)=b(a−b)(a−c)−c(a−c)(a−b)(a−b)(b−c)(c−a)=(a−b)(b−c)(a−c)(a−b)(b−c)(c−a)=−1Ta có a2(b−c)2+b2(c−a)2+c2(a−b)2=(ab−c+bc−a+ca−b)2−2P≥−2P=2
cái này là bđt x2+y2+z2=(x+y+z)2−2(xy+yz+zx)