Question

[Mai Anh]

Cho a + b + c = 2009. Chứng minh rằng:

Answer 1

[Acoustic]

Xét tử \(a^3+b^3+c^3-3abc\)

\(=\left(a+b\right)^3+c^3-3abc-3ab\left(a+b\right)\)

\(=\left(a+b+c\right)\left[\left(a+b\right)^2-c\left(a+b\right)+c^2\right]-3ab\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left[a^2+b^2+2ab-ac-bc+c^2\right]-3ab\left(a+b+c\right)\)

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

\(\Rightarrow A=\frac{\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)}{a^2+b^2+c^2-ab-bc-ca}=a+b+c=2009\)

Answer 2

[Hạ Băng]

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