Cho a+b+c=0 cmr a^4+b^4+c^4= 1/2(a^2+b^2+c^2)^2
a+b+c=0 => (a+b+c)2=0 => a2+b2+c2 = - 2(ab+bc+ca)
=>( a2+b2+c2 )2= 4(ab+bc+ca)2 = 4[b(a+c)2 +ca]2 =
a4+b4+c4 = 1/2 . (a2+b2+c2)2
<=> 2a4+2b4+2c4 = a4+b4+c4 + 2a2b2+2b2c2+2c2a2
<=> a4+b4+c4 = 2a2b2+2b2c2+2c2a2
<=> a4+b4 - 2a2b2 = 2b2c2+2c2a2 - c4
<=> (a2-b2)2 = c2(2b2 +2a2-c2)
<=> (a+b)2(a-b)2 = c2(2b2 +2a2-c2)
<=> (-c)2(a-b)2= c2(2b2 +2a2-c2)
<=> (a-b)2 = 2b2 +2a2-c2
<=> -2ab = b2 +a2-c2
<=> b2 +a2 +2ab = c2
<=> (a+b)2 = c2
=> a4+b4+c4 = 1/2 . (a2+b2+c2)2
