1. x² - 12x - 45 < 0
x² - 12x - 45 = 0
D = b² - 4ac = 12² + 4*45 = 144 + 180 = 324 = 18²>0
x1 =
x2 =
ответ: x∈(-3; 15)
2. (x+7)(x-5) > 0
x² - 5x + 7x - 35 > 0
x² + 2x - 35 > 0
x² + 2x - 35 = 0
D = b² - 4ac = 4 + 35 * 4 = 4 + 140 = 144 = 12²>0
ответ: x∈(-∞; -7) U (5; +∞)
1. x² - 12x - 45 < 0
x² - 12x - 45 = 0
D = b² - 4ac = 12² + 4*45 = 144 + 180 = 324 = 18²>0
x1 =![\frac{12 + 18}{2} = 15](/tpl/images/0079/3776/11eb9.png)
x2 =![\frac{12 - 18}{2} = -3](/tpl/images/0079/3776/3a329.png)
ответ: x∈(-3; 15)
2. (x+7)(x-5) > 0
x² - 5x + 7x - 35 > 0
x² + 2x - 35 > 0
x² + 2x - 35 = 0
D = b² - 4ac = 4 + 35 * 4 = 4 + 140 = 144 = 12²>0
x1 =![\frac{-2+12}{2} = 5](/tpl/images/0079/3776/c446b.png)
x2 =![\frac{-2-12}{2} = -7](/tpl/images/0079/3776/3b721.png)
ответ: x∈(-∞; -7) U (5; +∞)