Question

Решите по теореме Виета
х^2 -3x+a=0

Answer 1

$x^2 - 3x + a = 0\\ x_1 + x_2 = -b, x_1x_2 = a, x_1^2 + x_2^2 = 65\\ (x_1 + x_2)^2 = x_1^2 + 2x_1x_2 + x_2^2\\ frac{1}2left((x_1 + x_2)^2 - (x_1^2 + x_2^2)right) = x_1x_2\\ frac{9 - 65}{2} = -28 = a\\ x_1 + x_2 = 3 = -4 + 7, x_1x_2 = -28 = -4*7\\ boxed{x_1 = -4, x_2 = 7}$