Розділ 3. КВАДРАТНІ РІВНЯННЯ » 24.23 (1-3)

24.23 Скоротіть дріб: 1) (4x-12)/(x^2- 5x+6) = (4(x-3))/((x-3)(x-2)) = 4/(x-2). x2 – 5x + 6 = 0; D = (–5)2 – 4 • 6 = 1; x1 = (5+1)/2 = 3; x2 = (5-1)/2 = 2. 2) (x^2- x-12)/(x^2+ 3x) = ((x- 4)(x+3))/(x(x+3)) = (x-4)/x. x2 – x – 12 = 0; D = (–1)2 – 4 • (–12) = 49; x1 = (1+7)/2 = 4; x2 = (1-7)/2 = –3. 3) (2x^2+ 5x-3)/(x^2- 9) = (2(x- 1/2)(x+3))/((x-3)(x+3)) = (2x-1)/(x-3). 2x2 + 5x – 3 = 0; D = 52 – 4 • (–14) = 81; x1 = (-5+9)/2 = 2; x2 = (-5-9)/2 = –7.