![{x}^{2} y + x {y}^{2} - 3 - x - y + 3xy = \\ = xy(x + y) - (x + y) + 3 (xy - 1) = \\ = (x + y)(xy - 1) + 3(xy - 1) = \\ = (xy - 1)(x + y + 3) \\ \\](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D+y+%2B+x+%7By%7D%5E%7B2%7D++-+3+-+x+-+y+%2B+3xy+%3D++%5C%5C++%3D+xy%28x+%2B+y%29+-+%28x+%2B+y%29++%2B+3+%28xy+-+1%29+%3D++%5C%5C++%3D+%28x+%2B+y%29%28xy+-+1%29++%2B++3%28xy+-+1%29+%3D++%5C%5C++%3D+%28xy+-+1%29%28x+%2B+y+%2B+3%29+%5C%5C++%5C%5C+)
x=1,75=1. 3/4=7/4
y=3/7
![( \frac{7}{4} \times \frac{3}{7} - 1)( \frac{7}{4} + \frac{3}{7} + 3) = \\ = - \frac{1}{4} \times \frac{49 + 12 + 84}{28} = \\ = - \frac{145}{28} = - 5 \frac{5}{28}](https://tex.z-dn.net/?f=%28+%5Cfrac%7B7%7D%7B4%7D++%5Ctimes++%5Cfrac%7B3%7D%7B7%7D++-+1%29%28+%5Cfrac%7B7%7D%7B4%7D++%2B++%5Cfrac%7B3%7D%7B7%7D++%2B+3%29+%3D++%5C%5C++%3D++-++%5Cfrac%7B1%7D%7B4%7D++%5Ctimes++%5Cfrac%7B49+%2B+12+%2B+84%7D%7B28%7D++%3D++%5C%5C++%3D++-++%5Cfrac%7B145%7D%7B28%7D++%3D++-+5+%5Cfrac%7B5%7D%7B28%7D+)
Ответ: -5 целых 5/28
4)
![a {x}^{2} + bx + c = a(x - x_{1} )(x - x_{2} )](https://tex.z-dn.net/?f=a+%7Bx%7D%5E%7B2%7D++%2B+bx+%2B+c+%3D+a%28x+-+x_%7B1%7D+%29%28x+-+++x_%7B2%7D+%29)
![{x}^{2} - 5x + 6 = 0](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D++-+5x+%2B+6+%3D+0)
по теореме Виета найдем корни уравнения:
![x_{1} + x_{2} = 5 \\ x_{1} \times x_{2} = 6 \\ x_{1} = 2 \\ x_{2} = 3 \\ a = 1](https://tex.z-dn.net/?f=+x_%7B1%7D+%2B++x_%7B2%7D+%3D+5+%5C%5C+x_%7B1%7D++%5Ctimes+++x_%7B2%7D+%3D+6+%5C%5C+x_%7B1%7D++%3D+2+%5C%5C+x_%7B2%7D+%3D+3+%5C%5C+a+%3D+1)
Ответ:
![{x}^{2} - 5x + 6 = (x - 2)(x - 3)](https://tex.z-dn.net/?f=%7Bx%7D%5E%7B2%7D++-+5x+%2B+6+%3D+%28x+-+2%29%28x+-+3%29)
5)
![{x}^{2} + 29 = (x + 5)(x - 3) \\ {x}^{2} + 29 = {x}^{2} + 5x - 3x - 15 \\ 2x = 15 + 29 \\ 2x = 44 \\ x = 22](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D++%2B+29+%3D+%28x+%2B+5%29%28x+-+3%29+%5C%5C++%7Bx%7D%5E%7B2%7D++%2B+29+%3D++%7Bx%7D%5E%7B2%7D++%2B+5x+-+3x+-+15+%5C%5C+2x+%3D+++15+++%2B+29+%5C%5C+2x+%3D+44+%5C%5C+x+%3D+22)
Ответ: сторона квадрата равна 22.
В первый день x кг, во второй x+690 кг
x/3 = (x+690)/4
4x = 3x+2070
x = 2070 кг собрали в первый день
2070+690 = 2760 кг собрали во второй день.
1) 5*4=20 (руб) - стоимость 5 тетрадей
2) 4*7=28 (руб) - стоимость 4 блокнотов
3) 20/28=5/7 - отношение стоимости 5 тетрадей к стоимости 4 блокнотов
Ответ: 5/7