Question

Cho a+ b+ c =0. Chứng minh :a³+b³+c³=3abc

Answer 1

a + b + c = 0 \(\Rightarrow\) a + b = - c

a³ + b³ + c³ = (a + b)³ - 3ab(a + b) + c³

= (- c)³ - 3ab(- c) + c³

= 3abc

Answer 2

Vì a+b+c=0

\(\Rightarrow a+b=-c\)

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

\(\Rightarrow a^3+3a^2b+3ab^2+b^3=-c^3\)

=>a³+b³+c³=-3a²b-3ab²

^=-3ab(a+b)

^{Mà a+b=c}

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

=3abc(đpcm)

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