Question

If alpha and beta are the roots of the equation x^2-2x+4=0 ,then alpha^9+beta^9

Answer 1

Step-by-step explanation:

alpha + beta = 2

alpha × beta = 4

(alpha + beta)³ = alpha³ + beta³ + 3(4)(2)

8 = alpha³ + beta³ + 24

alpha³ + beta³ = -16

alpha^9 + beta^9 + 3(4)³(-16) = -4096

alpha^9 + beta^9 + 3(64)(-16) = -4096

alpha^9 + beta^9 = -4096 + 3072 = -1024