3 задача.
1) x^2 - 13x + 22 = 0
(x - 2)(x - 11) = 0
x1 = 2; x2 = 11
2) x^2 + 2x - 24 = 0
(x + 6)(x - 4) = 0
x1 = -6; x2 = 4
3) x^2 - 2x - 80 = 0
(x - 10)(x + 8) = 0
x1 = -8; x2 = 10
4) x^2 + 12x + 35 = 0
(x + 5)(x + 7) = 0
x1 = -7; x2 = -5
4 задача.
x1*x2 = c/a
x1 = -1
x2 = -c/a
а) 5x^2 - x - 6 = 0
x1 = -1; x2 = 6/5
в) -3x^2 + 13x + 16 = 0
x1 = -1; x2 = 16/3
5 задача. x^2 = px - 6 = 0
Нет, потому что произведение двух отрицательных чисел положительно,
а по теореме Виета x1*x2 = c/a = -6 отрицательно.
6 задача. x^2 + 5x + 2 = 0
1) x1^2*x2 + x1*x2^2 = x1*x2*(x1 + x2) = c/a*(-b/a) = 2/1*(-5/1) = -10
2) ![\frac{x1}{x2} + \frac{x2}{x1} +2= \frac{x1^2+x2^2+2x1*x2}{x1*x2}= \frac{(x1+x2)^2}{x1*x2} = \frac{(-b/a)^2}{c/a} = \frac{b^2}{a^2} \frac{a}{c}= \frac{b^2}{ac} = \frac{25}{2} \frac{x1}{x2} + \frac{x2}{x1} +2= \frac{x1^2+x2^2+2x1*x2}{x1*x2}= \frac{(x1+x2)^2}{x1*x2} = \frac{(-b/a)^2}{c/a} = \frac{b^2}{a^2} \frac{a}{c}= \frac{b^2}{ac} = \frac{25}{2}](https://tex.z-dn.net/?f=+%5Cfrac%7Bx1%7D%7Bx2%7D+%2B+%5Cfrac%7Bx2%7D%7Bx1%7D+%2B2%3D+%5Cfrac%7Bx1%5E2%2Bx2%5E2%2B2x1%2Ax2%7D%7Bx1%2Ax2%7D%3D+%5Cfrac%7B%28x1%2Bx2%29%5E2%7D%7Bx1%2Ax2%7D+%3D+%5Cfrac%7B%28-b%2Fa%29%5E2%7D%7Bc%2Fa%7D+%3D+%5Cfrac%7Bb%5E2%7D%7Ba%5E2%7D+%5Cfrac%7Ba%7D%7Bc%7D%3D+%5Cfrac%7Bb%5E2%7D%7Bac%7D+%3D+%5Cfrac%7B25%7D%7B2%7D+)