Предмет: Математика,
автор: yanko041
Помогите пожалуйста с 31 и с 32 заданием. Заранее спасибо)
Приложения:
![](https://files.topotvet.com/i/834/8347685571306a938238387fb89a2c90.jpg)
Ответы
Автор ответа:
0
1)![x^2 + x + frac{4}{x} ( frac{1}{2} + frac{1}{x}) = 16 x^2 + x + frac{4}{x} ( frac{1}{2} + frac{1}{x}) = 16](https://tex.z-dn.net/?f=x%5E2+%2B+x+%2B+frac%7B4%7D%7Bx%7D+%28+frac%7B1%7D%7B2%7D+%2B+frac%7B1%7D%7Bx%7D%29+%3D+16+)
![x^2+x+ frac{4}{x} ( frac{x}{2x} + frac{2}{2x} ) = 16 x^2+x+ frac{4}{x} ( frac{x}{2x} + frac{2}{2x} ) = 16](https://tex.z-dn.net/?f=x%5E2%2Bx%2B+frac%7B4%7D%7Bx%7D+%28+frac%7Bx%7D%7B2x%7D+%2B+frac%7B2%7D%7B2x%7D+%29+%3D+16)
![frac{2x^3}{2x} + frac{2x^2}{2x} + frac{8x(x+2)}{2x} - frac{32x}{2x} = 0 frac{2x^3}{2x} + frac{2x^2}{2x} + frac{8x(x+2)}{2x} - frac{32x}{2x} = 0](https://tex.z-dn.net/?f=+frac%7B2x%5E3%7D%7B2x%7D+%2B+frac%7B2x%5E2%7D%7B2x%7D+%2B+frac%7B8x%28x%2B2%29%7D%7B2x%7D+-+frac%7B32x%7D%7B2x%7D+%3D+0)
![frac{2x^3+2x^2+8x^2+16x-32x}{2x} = 0 frac{2x^3+2x^2+8x^2+16x-32x}{2x} = 0](https://tex.z-dn.net/?f=+frac%7B2x%5E3%2B2x%5E2%2B8x%5E2%2B16x-32x%7D%7B2x%7D+%3D+0)
![frac{x(2x^2+10x-16}{2x} = 0 frac{x(2x^2+10x-16}{2x} = 0](https://tex.z-dn.net/?f=+frac%7Bx%282x%5E2%2B10x-16%7D%7B2x%7D+%3D+0)
2x² + 10x - 16 = 0
D = (10)² - 4 * 2 * (-16) = 228
x =![frac{-10б2 sqrt{57} }{4} frac{-10б2 sqrt{57} }{4}](https://tex.z-dn.net/?f=+frac%7B-10%D0%B12+sqrt%7B57%7D+%7D%7B4%7D+)
x =![frac{-5б sqrt{57} }{2} frac{-5б sqrt{57} }{2}](https://tex.z-dn.net/?f=+frac%7B-5%D0%B1+sqrt%7B57%7D+%7D%7B2%7D+)
x1 = 2,5 +
x2 = 2,5 -![sqrt{57} sqrt{57}](https://tex.z-dn.net/?f=+sqrt%7B57%7D+)
2)![frac{3x}{x^2-8x+12} = frac{3x+2x}{x^2-8x+12+2x} = frac{5x}{x^2-6x+12} frac{3x}{x^2-8x+12} = frac{3x+2x}{x^2-8x+12+2x} = frac{5x}{x^2-6x+12}](https://tex.z-dn.net/?f=+frac%7B3x%7D%7Bx%5E2-8x%2B12%7D+%3D+frac%7B3x%2B2x%7D%7Bx%5E2-8x%2B12%2B2x%7D+%3D+frac%7B5x%7D%7Bx%5E2-6x%2B12%7D+)
![frac{x^2-10x+12}{x^2-6x+12} = frac{5x}{x^2-6x+12} frac{x^2-10x+12}{x^2-6x+12} = frac{5x}{x^2-6x+12}](https://tex.z-dn.net/?f=+frac%7Bx%5E2-10x%2B12%7D%7Bx%5E2-6x%2B12%7D+%3D+frac%7B5x%7D%7Bx%5E2-6x%2B12%7D+)
x² - 10x + 12 = 5x
x² - 15x + 12 = 0
D = (-15)² - 4 * 1 * 12 = 177
x =![frac{15б sqrt{177} }{2} frac{15б sqrt{177} }{2}](https://tex.z-dn.net/?f=+frac%7B15%D0%B1+sqrt%7B177%7D+%7D%7B2%7D+)
x =![frac{15б13,3}{2} frac{15б13,3}{2}](https://tex.z-dn.net/?f=+frac%7B15%D0%B113%2C3%7D%7B2%7D+)
x1 = 14,15
x2 = 0,85
14,15 + 0,85 = 15
2x² + 10x - 16 = 0
D = (10)² - 4 * 2 * (-16) = 228
x =
x =
x1 = 2,5 +
x2 = 2,5 -
2)
x² - 10x + 12 = 5x
x² - 15x + 12 = 0
D = (-15)² - 4 * 1 * 12 = 177
x =
x =
x1 = 14,15
x2 = 0,85
14,15 + 0,85 = 15
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