Vì a + b + c + d = 0 nên a + b = -(c+d)
$\Leftrightarrow (a+b)^3 = -(c+d)^3$
$\Leftrightarrow (a+b)^3 + (c+d)^3 = 0$
$\Leftrightarrow a^3 + b^3 + 3ab(a+b) + c^3 + d^3 + 3cd(c+d) = 0$
$\Leftrightarrow a^3 + b^3 + c^3 + d^3 = -3[ab(a+b)+cd(c+d)]$
Mà a+b = -(c+d) $\Rightarrow a^3 + b^3 + c^3 + d^3 = -3(ab-cd)(a+b) = 3(ab-cd)(c+d)$
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- huykinhcan99 yêu thích