Đặt `P =a^4(b-c)+b^4(c-a)+c^4(a-b)`

`=a^4(b-c)-b^4[(a-b)+(b-c)]+c^4(a-b)`

`=(b-c)(a^4-b^4)-(a-b)(b^4-c^4)`

`=(a-b)(b-c)[(a+b)(a^2+b^2)-(b+c)(b^2+c^2)]`

`=(a-b)(b-c)[(a^3-c^3)+b(a^2-c^2)+b^2(a-c)]`

`=-(a-b)(b-c)(c-a)(a^2+b^2+c^2+ab+bc+ca)`

`=-1/2(a-b)(b-c)(c-a)[(a+b)^2+(b+c)^2+(c+a)^2]`

`P=0<=>[(a-b=0),(b-c=0),(c-a=0),(\underbrace{(a+b)^2}_{>=\ 0}+\underbrace{(b+c)^2}_{>=\ 0} +\underbrace{(c+a)^2}_{>=\ 0}=0):}`

`<=>[(a=b),(b=c),(c=a),(a+b=b+c=c+a=0):}`

`<=>[(a=b),(b=c),(c=a),(a=b=c=0):}` (vô lí vì `a ne b ne c`)

Vậy `P ne 0`, ĐPCM