Equating
coefficients in
(x  A)(x  B)(x  C) = x^{3}  8x^{2} + 5x + 12 gives:
A + B + C = 8, AB + BC + CA = 5, ABC = 12.
Using these values in the following identity:
A^{4} + B^{4} + C^{4} = (A + B + C)^{4} – 4(A +
B + C)^{2}(AB + BC + CA)
+2(AB + BC + CA)^{2}
+ 4ABC(A + B + C)
A^{4} + B^{4} + C^{4} =
8^{4}  4*8^{2}*5 + 2*5^{2}  4*12*8
= 2482

Posted by Harry
on 20150705 17:25:49 