A,B,C are real values such that
A + B + C = 2,
A2 + B2 + C2 = 6,
A3 + B3 + C3 = 8
then find the value of A4 + B4 + C4
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3 Answers
101A^2 +B^2+C^2=6
(A+B+C)^2 -2(AB+BC+CA)=6
SO, AB+BC+CA=(-1)
A^3+B^3+C^3=8
OR (A+B+C)( A^2+B^2+C^2-(AB+BC+CA) )+3ABC
from here we get ABC=(-2)
so, A^4+B^4+C^4
={A^2+B^2+C^2}^2 -2{A^2B^2+B^2C^2+C^2A^2}
we put the values of AB+BC+CA and ABC and A^2+B^2+C^2
we get A^4+B^4+C^4=18
