Question

Cho a+b+c=0.Chứng minh rằng M=N=P với :

M=a(a+b)(a+c) ; N=b(b+c)(b+a) ; P=c(c+a)(c+b)

Answer 1

Ta có: \(a+b+c=0\)

=> \(a+b=-c;a+c=-b;b+c=-a\)

Do đó:

\(M=a\left(a+b\right)\left(a+c\right)=a\left(-c\right)\left(-b\right)=abc\)

\(N=b\left(b+c\right)\left(b+a\right)=b\left(-a\right)\left(-c\right)=abc\)

\(P=c\left(c+a\right)\left(c+b\right)=c\left(-b\right)\left(-a\right)=abc\)

=> M=N=P ( = abc)

Answer 2

Ta có : a + b + c = 0

=> a + b = -c ; a + c = -b ; b + c = -a

Thế vào M, N, P :

=> M = a.(-c).(-b) = -abc

N = b.(-a).(-c) = -abc

P = c.(-b).(-a) = -abc

Vậy M = N = P.