A, B and C are roots of the equation: x³ - 8x² + 5x +12 = 0

Without solving the above equation, find the value of :
A⁴ + B⁴ + C⁴

Equating coefficients in

(x - A)(x - B)(x - C) = x³ - 8x² + 5x + 12    gives:


A + B + C = 8,    AB + BC + CA = 5,    ABC = -12.

Using these values in the following identity:

A⁴ + B⁴ + C⁴ = (A + B + C)⁴ – 4(A + B + C)²(AB + BC + CA)

                        +2(AB + BC + CA)² + 4ABC(A + B + C)

A⁴ + B⁴ + C⁴      = 8⁴ - 4*8²*5 + 2*5² - 4*12*8

                        = 2482

Posted by Harry on 2015-07-05 17:25:49