РОЗДІЛ 4. Квадратні рівняння » 818 (1-2)

818. Скоротіть дріб: 1) (3х-1)/(〖3х〗^2+2х-1) = (3х-1)/((3х-1)(х+1)) = 1/(х+1); 3x² + 2x – 1 = 3(x – 1/3)(x + 1) = (3x – 1)(x + 1); D = 22 – 4 • 3 • (–1) = 4 + 12 = 16. x1 = (-2-√16)/(2•3) = (-2-4)/6 = (-6)/6 = –1; x2 = (-2+√16)/(2•3) = (-2+4)/6 = 2/6 = 1/3. 2) (〖2х〗^2-5х-3)/(6х-18) = ((2х+1)(х-3))/(6(х-3)) = (2х+1)/6; 2x² – 5x – 3 = 2(x + 1/2)(x – 3) = (2x + 1)(x – 3); D = (–5)2 – 4 • 3 • (–3) = 25 + 24 = 49; x1 = (5-√49)/(2•2) = (5-7)/4 = (-2)/4 = –1/2; x2 = (5+√49)/(2•2) = (5+7)/4 = 12/4 = 3.