ta có :
`(2a^3)/(b^3+2c^3)+(2b^3)/(c^3+2a^3)+(2c^3)/(a^3+2b^3)`
đặt :
`x=b^3+2c^3`
`y=c^3+2a^3`
`z=a^3+2b^3`
`⇒(2a^3)/(b^3+2c^3)+(2b^3)/(c^3+2a^3)+(2c^3)/(a^3+2b^3)=(2(z-2x+4y))/(9x)+(2(x-2y+4z))/(9y)+(2(y-2z+4x))/(9z)=2/9[ (z/x y/z x/y)+4 (z/x y/z x/y)-6]≥2/9 (3+4.3-6)=2`
`(a^4(b^2+c^2))≥2a^3`
`(b^4(c^2+a^2))≥2b^3`
`(c^4(a^2+c^2))≥2c^3`
`⇒(a^4(b^2+c^2))/(b^3+2c^3)+(b^4(c^2+a^2))/(c^3+2a^3)+(c^4(a^2+c^2))/(a^3+2b^3)≥(2a^3)/(b^3+2c^3)+(2b^3)/(c^3+2a^3)+(2c^3)/(a^3+2b^3)≥2`
`''=''`xẩy ra khi :
`a=b=c=1`
