Розділ 3. КВАДРАТНІ РІВНЯННЯ » 24.25

Обчисліть значення дробу: 1) (2x^2+ 9x-5)/(x^2+ 8x+15) = (2(x- 1/2)(x+5))/((x+3)(x+5)) = (2x-1)/(x+3). 2x2 + 9x – 5 = 0; D = 92 – 4 • 2 • (–5) = 121; √D = 11; x1 = (-9+11)/(2 • 2) = 1/2; x2 = (-9-11)/4 = –5. x2 + 8x + 15 = 0; D = 82 – 4 • 15 = 4; x1 = (-8+2)/2 = –3; x2 = (-8-2)/2 = –5. Якщо х = 97, то (2x-1)/(x+3) = (2 • 97-1)/(97+3) = 193/100 = 1,93. 2) (3x^2- 24x + 48)/(7x-3x^2+ 20) = (3(x-4)^2)/(-3(x-4)(x+ 5/3)) = (x-4)/(-(x+ 5/3)) = (x-4)/(-(x+ 5/3)) = (4-x)/(x+ 5/3). 3x2 – 24x + 48 = 3(x2 – 8x + 16) = 3(x – 4)2; 7x – 3x2 + 20 = 3x2 – 7x – 20 = 0; D = (–7)2 – 4 • 3 • (–20) = 289; √D = 17; x1 = (7+17)/6 = 4; x2 = (7-17)/6 = –10/6 = –5/2. Якщо х = –2/3, то (4-x)/(x+ 5/3) = (4+ 2/3)/(-2/3+ 5/3) = 42/3.