a + b + c = 0
=> (a + b + c)2 = 0
=> a2 + b2 + c2 + 2ab + 2bc + 2ca = 0
=> a2 + b2 + c2 = -2(ab + 2bc + 2ca)
=> (a2 + b2 + c2)2 = [-2(ab + bc + ca)]2
=> a4 + b4 + c4 + 2a2b2 + 2b2c2 + 2c2a2 = 4(a2b2 + b2c2 + c2a2 + 2ab2c + 2a2bc + 2abc2)
=> a4 + b4 + c4 = 4a2b2 + 4b2c2 + 4c2a2 + 8a2bc + 8ab2c + 8abc2 - 2a2b2 - 2b2c2 - 2a2c2
=> a4 + b4 + c4 = 2a2b2 + 2b2c2 + 2c2a2 + 8abc(a + b + c)
=> a4 + b4 + c4= 2a2b2 + 2b2c2 + c2a2
=> a4 + b4 + c4 = 2a2b2 + 2b2c2 + 2c2a2 + 2abc(a + b + c) (Vì a + b + c = 0)
=> a4 + b4 + c4 = 2a2b2 + 2b2c2 + 2c2a2 + 2a2bc + 2ab2c + 2abc2
=> a4 + b4 + c4 = 2(a2b2 + b2c2 + c2a2 + a2bc + ab2c + abc2)
=> a4 + b4 + c4 = 2(ab + bc + ca)2 (đpcm)
