Question

[tran thi tHanh tAM]

cho A+B+C=0 và AB+AC+BC=0

TÍNH  M=\(\left(A-2018\right)^{2019}+\left(B-2018\right)^{2019}-\left(C+2018\right)^{2019}\)

Answer 1

[tth_new]

Ta có: \(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ac\)

\(\Rightarrow a^2+b^2+c^2=\left(a+b+c\right)^2-2\left(ab+bc+ac\right)\)

hay \(a^2+b^2+c^2=0\Rightarrow a=b=c=0\)

Thay a = b = c = 0 vào M rồi tính như bình thường nha bạn!

Answer 2

[Phùng Minh Quân]

Ta có : 

\(a+b+c=0\)

\(\Leftrightarrow\)\(\left(a+b+c\right)^2=0\)

\(\Leftrightarrow\)\(a^2+b^2+c^2+2ab+2bc+2ca=0\)

\(\Leftrightarrow\)\(a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)

\(\Leftrightarrow\)\(a^2+b^2+c^2=0\)

\(\Leftrightarrow\)\(\hept{\begin{cases}a^2=0\\b^2=0\\c^2=0\end{cases}\Leftrightarrow a=b=c=0}\)

\(\Rightarrow\)\(M=\left(a-2018\right)^{2019}+\left(b-2018\right)^{2019}-\left(c+2018\right)^{2019}\)

\(\Rightarrow\)\(M=-2018^{2019}-2018^{2019}-2018^{2019}\)

\(\Rightarrow\)\(M=-3.2018^{2019}\)

Chúc bạn học tốt ~