Розділ 3. КВАДРАТНІ РІВНЯННЯ » 24.24

Скоротіть дріб: 1) (x^2+ 6x+5)/(x^2+ 5x) = ((x+1)(x+5))/(x(x+5)) = (x+1)/x. x2 + 6x + 5 = 0; D = 62 – 4 • 5 = 16; x1 = (-6+4)/2 = –1; x2 = (-6-4)/2 = –5. 2) (x^2- 16)/(3x^2- 10x-8) = ((x-4)(x+4))/(3(x-4)(x+ 2/3)) = (x+4)/(3x+2). 3x2 – 10x – 8 = 0; D = (–10)2 – 4 • 3 • (–8) = 196; √D = 14; x1 = (10+14)/6 = 4; x2 = (10-14)/6 = –2/3. 3) (x^2+ x-6)/(x^2- 7x+10) = ((x-2)(x+3))/((x-5)(x-2)) = (x+3)/(x-5). x2 + x – 6 = 0; D = 12 – 4 • (–6) = 25; x1 = (-1+5)/2 = 2; x2 = (-1-5)/2 = –3. x2 – 7x + 10 = 0; D = (–7)2 – 4 • 10 = 9; x1 = (7+3)/2 = 5; x2 = (7-3)/2 = 2. 4) (2x^2+ 4x+2)/(3x^2- 6x-9) = (2(x+1)^2)/(3(x-3)(x+1)) = (2(x+1))/(3(x-3)). 2x2 + 4x + 2 = 2(x2 + 2x + 1) = 2(x + 2)2; 3x2 – 6x – 9 = 0; x2 – 2x – 3 = 0; D = (–2)2 – 4 • (–3) = 16; x1 = (2+4)/2 = 3; x2 = (2-4)/2 = –1.