Question

Не решая уравнения x^2-5x-2=0 найти a) x1^2+x2^2
Б) x1^3+x2^3

Answer 1

x1+x2=2,5

x1*x2 = -1

x1^2+x2^2 = (x1+x2)^2 - 2x1*x2 = 6,25 + 2 = 8,25

x1^3+x2^3 = (x1+x2)(x1^2 - x1*x2 + x2^2) = 2,5* 9,25 =5/2 * 37/4 = 185/8 = 23 1/8