Question

[Ba Dấu Hỏi Chấm]

CHO  x= \(\frac{a+b+c}{2}\). CMR : (x - a) (x-b) + (x-b) (x - c) + (x - c) (x - a)  =   ab + bc + ca - x²

Answer 1

[Lê Chí Cường]

Ta có: VT=(x-a).(x-b)+(x-b).(x-c)+(x-c).(x-a)

              =x²-ax-bx+ab+x²-bx-cx+bc+x²-cx-ax+ca

              =3.x²-2.(ax+bx+cx)+ab+bc+ca

              =3.x²-2x.(a+b+c)+ab+bc+ca

              =x.[3x-2.(a+b+c)]+ab+bc+ca

Vì \(x=\frac{a+b+c}{2}\)

<=>a+b+c=2x

<=>2.(a+b+c)=4x

<=>3x-2.(a+b+c)=-x

=>VT=x.(-x)+ab+bc+ca

        =ab+bc+ca-x²=VP

=>ĐPCM

Answer 2

[Ba Dấu Hỏi Chấm]

oh thanks you ~~~~