Question

Answer 1

`a^3+b^3+c^3=3abc`

`=>a^3+b^3+c^3-3abc=0`

`=>(a+b)^3-3ab(a+b)-3abc+c^3=0`

`=>(a+b+c)[(a+b)^2-c(a+b)+c^2]-3ab(a+b+c)=0`

`=>(a+b+c)(a^2+b^2+c^2-ac-bc+c^2-3ab)=0`

`=>(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=0`

`TH1:a+b+c=0`

`=>a+b=-c`

`=>a^2+2ab+b^2=c^2`

`=>a^2+b^2-c^2=-2ab`

Tương tự ta được: `a^2+c^2-b^2=-2ac;b^2+c^2-a^2=-2bc`

`=>D=(ab^2)/(-2ab)+(bc^2)/(-2bc)+(ca^2)/(-2ac)`

`=-(a+b+c)/2=0`

`TH2:a^2+b^2+c^2-ac-ab-bc=0`

`=>2a^2+2b^2+2c^2-2ac-2ab-2bc=0`

`=>(a-b)^2+(b-c)^2+(c-a)^2=0`

`=>{(a-b=0),(b-c=0),(c-a=0):}` (vô lý)

Vậy: `D=0`

Answer 2

\(=\frac{c}{a}\) bạn nhé