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Question

cho a+b+c=0.CM:a3+b3+c3=3abc

Chippy Linh · Accepted Answer

$a+b+c=0\$

$\Rightarrow\left(a+b+c\right)^3=0$

$\Rightarrow a^3+b^3+c^3+3a^2b+3ab^2+3b^2c+3bc^2+3a^2c+3ac^2+6abc=0$

=>  $a^3+b^3+c^3+\left(3a^2b+3ab^2+3abc\right)+\left(3b^2c+3bc^2+3abc\right)+\left(3a^2c+3ac^2+3abc\right)-3abc=0$

$\Rightarrow a^3+b^3+c^3+3ab\left(a+b+c\right)+3bc\left(a+b+c\right)+3ac\left(a+b+c\right)=3abc$

$Do$ $a+b+c=0$

$\Rightarrow a^3+b^3+c^3=3abc$(đpcm)Câu trả lời: $a+b+c=0\$

$\Rightarrow\left(a+b+c\right)^3=0$

$\Rightarrow a^3+b^3+c^3+3a^2b+3ab^2+3b^2c+3bc^2+3a^2c+3ac^2+6abc=0$

=>  $a^3+b^3+c^3+\left(3a^2b+3ab^2+3abc\right)+\left(3b^2c+3bc^2+3abc\right)+\left(3a^2c+3ac^2+3abc\right)-3abc=0$

$\Rightarrow a^3+b^3+c^3+3ab\left(a+b+c\right)+3bc\left(a+b+c\right)+3ac\left(a+b+c\right)=3abc$

$Do$ $a+b+c=0$

$\Rightarrow a^3+b^3+c^3=3abc$(đpcm)

Nguyễn Xuân Tiến 24 · Answer

Cách này nhanh hơn nè bn!

$a+b+c=0\Rightarrow c=-\left(a+b\right)$

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

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

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

$=-3ab\left(a+b\right)=-3ab.-c=3abc$Câu trả lời: Cách này nhanh hơn nè bn!

$a+b+c=0\Rightarrow c=-\left(a+b\right)$

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

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

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

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

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