ta co :a + b+c=0
=>(a+b+c)^3= 0
<=> a^3 + b^3 + c^3 + 3a^2b+3a^2c + 3b^2a+3b^2c + 3c^2a+3c^2b + 6abc =0
<=>(a^3+b^3+c^3) + (3a^2b+3a^2c+3abc ) +(3b^2a+3b^c +3abc) +(3c^2a+3c^b +3abc ) - 3abc=0
<=>(a^3+b^3+c^3) + 3a(ab+ac+bc) + 3b(ab+bc+ac) + 3c(ac+bc+ab) - 3abc=0
<=>(a^3+b^3+c^3) +3(ab+bc+ac)(a+b+c) -3abc=0
<=>(a^3+b^3+c^3) +3(ab+bc+ac).0 - 3abc =0
<=> a^3+b^3+c^3 -3abc=0
=>a^3+b^3+c^3 =3abc (dpcm)
Ta co
\(a^3+b^3+c^3-3abc\)
=\(\left(a+b\right)^3+c^3-3ab\left(a+b\right)-3abc\)
=\(\left(a+b+c\right)\left[\left(a+b\right)^2-\left(a+b\right)c+c^2\right]-3ab\left(a+b+c\right)\)
=\(\left(a+b+c\right)\left[\left(a+b\right)^2-\left(a+b\right)c+c^2-3ab\right]\)
Ma a+b+c=3
=>\(a^3+b^3+c^3-3abc=0\)
=>\(a^3+b^3+c^3=3abc\)(\(ĐPCM\))
