Question

cho a +b + c = 0 chương minh 3abc = a³ +b³ +c³

Answer 1

vì a+b+c=0 => a=0;b=0;c=0

do đó a³=0³=0;b³=0³=0;c³=0³=0

 Vậy 3abc=3x0=0

Answer 2

Ta có

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

= (a + b + c)(a² + b² + 2ab - ac - bc + c²) - 3ab(a + b + c)

= (a + b + c)(a² + b² + c² - ab - bc - ac) = 0

=> a³ + b³ + c³ = 3abc