Question

Alpha and beta are the roots of the equation x2 + 2x + 1 = 0. Find alpha raise to 15 + beta raise to 15.

Answer 1

${x}^{2} + 2x + 1 = 0 \\ {(x + 1)}^{2} = 0 \\ x = - 1 \\ so \\ \alpha = \beta = - 1 \\ therefore \\ { \alpha }^{15} + { \beta }^{15} = {( - 1)}^{15} + {( - 1)}^{15} = - 1 - 1 = - 2 \\ { \alpha }^{15} + { \beta }^{15} = - 2$