Розділ 3. КВАДРАТНІ РІВНЯННЯ » 24.26 (3-4)

3) (x+4)/(3x+2) • (3x^2- 10x-8)/(x^2- 16). 3x2 – 10x – 8 = 0; D = (10)2 – 4 • 3 • (–8) = 196; √D = 14; x1 = (10+14)/6 = 4; x2 = (10-14)/6 = –2/3. (x+4)/(3x+2) • (3x^2- 10x-8)/(x^2- 16) = ((x+4) • 3(x-4)(x+ 2/3))/((3x+2)(x-4)(x+4)) = (3x+2)/(3x+2) = 1. 4) (-2x^2+ 5x-2)/(2x+10) : (2x^2+ 5x-3)/(x^2- 25). –2x2 + 5x – 2 = 0; 2x2 – 5x + 2 = 0; D = (–5)2 – 4 • 2 • 2 = 9; x1 = (5+3)/4 = 2; x2 = (5-3)/4 = 1/2. 2x2 + 5x – 3 = 0; D = 52 – 4 • 2 • (–3) = 49; x1 = (-5+7)/4 = 1/2; x2 = (-5-7)/4 = –3. (-2x^2+ 5x-2)/(2x+10) : (2x^2+ 5x-3)/(x^2- 25) = (-2(x-2)(x- 1/2)(x-5)(x+5))/(2(x+5) • 2(x- 1/2)(x+3)) = ((x-2)(5-x))/(2(x+3)).