Розділ 3. КВАДРАТНІ РІВНЯННЯ » 24.23 (3-6)

4) (x^2- 4x+4)/(x^2+ 5x-14) = ((x-2)^2)/((x-2)(x+7)) = (x-2)/(x+7). x2 + 5x – 14 = 0; D = 52 – 4 • (–14) = 81; x1 = (-5+9)/2 = 2; x2 = (-5-9)/2 = –7. 5) (〖2x〗^2+ 9x-5)/(〖3x〗^2+ 14x-5) = (2(x- 1/2)(x+5))/(3(x- 1/3)(x+5)) = (2x-1)/(3x-1). 2x2 + 9x – 5 = 0; D = 92 – 4 • 2 • (–5) = 121; √D = 11; x1 = (- 9+11)/4 = 1/2; x2 = (-9-11)/4 = –5. 3x2 + 14x – 5 = 0; D = 142 – 4 • 3 • (–5) = 256; √D = 16; x1 = (-14+16)/6 = 1/3; x2 = (-14-16)/6 = –5. 6) (5x^2- 37x+14)/(22x-2x^2- 56) = (5(x-7)(x-0,4))/(-2(x-7)(x-4)) = (5x-2)/(8-2x). 5x2 – 37x + 14 = 0; D = (–37)2 – 4 • 5 • 14 = 1089; √D = 33; x1 = (37+33)/10 = 7; x2 = (37-33)/10 = 0,4. 22x – 2x2 – 56 = 0; x2 – 11x + 28 = 0; D = (–11)2 – 4 • 28 = 9; x1 = (11+3)/2 = 7; x2 = (11-3)/2 = 4.