Question

Cho a+b+c+d = 0

CMR : a³+b³+c³+d³ = 3(ab - cd)(c+d)

HELP ME !!!!!

Answer 1

a+b+c+d=0

=>a+b=-(c+d)

=>(a+b)^3=-(c+d)^3

=> a^3+b^3+3ab(a+b)=-c^3-d^3-3cd(c+d)

=>a^3+b^3+c^3+d^3=-3ab(a+b)-3cd(c+d)

=>a^3+b^3+c^3+d^3=3ab(c+d)-3cd(c+d) vi a+b=-(c+d)

=> a^3+b^3+c^3+d^3=3(c+d)(ab+cd)

Xem lai gium mk nha!!

Answer 2

Ta có : a+b+c+d=0
=>a+b=-(c+d)
=> (a+b)^3=-(c+d)^3
=> a^3+b^3+3ab(a+b)=-c^3-d^3-3cd(c+d)
=> a^3+b^3+c^3+d^3=-3ab(a+b)-3cd(c+d)
=> a^3+b^3+c^3+d^3=3ab(c+d)-3cd(c+d) ( vi a+b = - (c+d))
==> a^3 +b^^3+c^3+d^3==3(c+d)(ab-cd)