If a + b + c = 0

  a2 + b2 + c2 = 6 

Find a4 + b4 +c4

Asked by poonambarnwal2018 | 23rd Apr, 2020, 02:49: PM

Expert Answer:

Given: a+b+c=0 ... (i) and a2+b2+c2=6 ... (ii)
From (i)
(a+b+c)2=0
a2+b2+c2+2(ab+bc+ac)=0
6+2(ab+bc+ac)=0 ... Using (ii)
ab+bc+ca=-3
Taking square of the above equation, we have
(ab+bc+ca)2=9
a2b2+b2c2+c2a2+2ab2c+2abc2+2a2bc=9

a2b2+b2c2+c2a2+2abc(a+b+c)=9
a2b2+b2c2+c2a2+2abc(0)=9    ... Using (i)
a2b2+b2c2+c2a2=9 ... (iii)
From (ii),
a2+b2+c2=6
(a2+b2+c2)2=36
a4+b4+c4+2(a2b2+b2c2+c2a2)=36
a4+b4+c4+2(9)=36 ... From (iii)
a4+b4+c4+18=36
a4+b4+c4=18

Answered by Renu Varma | 24th Apr, 2020, 11:25: AM

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