Задачі і вправи для повторення » 43

43. Скоротіть дріб: 1) (x+1)/(〖3x〗^2+ 5x+2) = (x+1)/((3x+2)(x+1)) = 1/(3x+2); 3x2 + 5x + 2 = 3(x + 2/3)(x + 1) = (3x + 2)(x + 1); D = 52 – 4 • 3 • 2 = 25 – 24 = 1; x1 = (-5- √1)/(2 •3) = (-5-1)/6 = (-6)/6 = –1; x2 = (-5 + √1)/(2 • 3) = (-5+1)/(2 •3) = (-4)/6 = –2/3; 2) (x^2- 11x-26)/(x^2- 4) = ((x+2)(x-13))/((x-2)(x+2)) = (x-13)/(x-2). x2 – 11x – 26 = (x + 2)(x – 13); x1 + x2 = 11; x1 • x2 = –26; x1 = –2; x2 = 13. 3) (〖6x〗^2- 17x+5)/(3x- 1) = ((3x-1)(2x-5))/(3x-1) = 2x – 5. 6x2 – 17x + 5 = 6(x – 1/3)(x – 5/2) = 3(x – 1/3) • 2(x – 5/2) = (3x – 1)(2x – 5); D = (–17)2 – 4 • 6 • 5 = 289 – 120 = 169; x1 = (17- √169)/(2 •6) = (17-13)/12 = 4/12 = 1/3; x2 = (17 + √169)/(2 • 6) = (17+13)/12 = 30/12 = 5/2; 4) (x^2- 6x+8)/(x^2- 3x-4) = ((x-2)(x-4))/((x+1)(x-4)) = (x-2)/(x+1). x2 – 6x + 8 = (x – 2)(x – 4); x1 + x2 = 6; x1 • x2 = 8; x1 = 2; x2 = 4. x2 – 3x – 4 = (x + 1)(x – 4); x1 + x2 = 3; x1 • x2 = –4; x1 = –1; x2 = 4.