If alpha and beta are the roots of the equation ax2 + bx + c = 0 and Sn = (alpha)n + (beta)n, show that aSn+1 + bSn + cSn-1 = 0 and hence find S5.
If alpha and beta are the roots of the equation ax2 + bx + c = 0 and Sn = (alpha)n + (beta)n, show that aSn+1 + bSn + cSn-1 = 0 and hence find S5.