60 : 15 = 4
60 : 20 = 3
<span>4 + 3 = 7</span>
12х-х=55
11х=55
х=55:11
х=5
2(х+3)=16
2х+6=16
2х=16-6
2х=10
х=10:2
х=5
5(х+3)+7=3(х+12)
5х+15+7=3х+36
5х-3х=36-15-7
2х=14
х=14:2
х=7
1)----
![\left \{ {{x+3xy+y=-19} \atop {xy+6=0}} \right. \\\\ xy = -6\\ x+3xy+y = x+y-18 = -19\\ x+y = -1\\\\ \left \{ {{x+y=-1} \atop {xy=-6}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%2B3xy%2By%3D-19%7D+%5Catop+%7Bxy%2B6%3D0%7D%7D+%5Cright.+%5C%5C%5C%5C%0Axy+%3D+-6%5C%5C%0Ax%2B3xy%2By+%3D+x%2By-18+%3D+-19%5C%5C%0Ax%2By+%3D+-1%5C%5C%5C%5C%0A+%5Cleft+%5C%7B+%7B%7Bx%2By%3D-1%7D+%5Catop+%7Bxy%3D-6%7D%7D+%5Cright.+)
По обратной теореме Виета, если сумма чисел равна -1 а их произведуние -6, то сами числа - это корни квадратного уравнения
![t^2+t-6 = 0\\ (t+3)(t-2) = 0\\\\ \left [ {{t=-3} \atop {t=2}} \right.](https://tex.z-dn.net/?f=+t%5E2%2Bt-6+%3D+0%5C%5C%0A%28t%2B3%29%28t-2%29+%3D+0%5C%5C%5C%5C%0A+%5Cleft+%5B+%7B%7Bt%3D-3%7D+%5Catop+%7Bt%3D2%7D%7D+%5Cright.)
Отсюда два решения: x = -3; y=2 ИЛИ x = 2;y=-3
2)----
![\left \{ {{3x+y=-4} \atop {\frac{7}{x+2}-\frac{10}{y} = 6}} \right. \\\\ y = -4-3x\\\\ \frac{7}{x+2}-\frac{10}{y} = \frac{7}{x+2}+\frac{10}{4+3x} = 6\\\\ 7(4+3x)+10(x+2) = 6(x+2)(4+3x)\\ 48+31x = 18x^2+60x+48\\ 18x^2+29x = 0\\\\ x = 0; y = -4\\ x = -29/18; y = -4+29/6 = 5/6](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B3x%2By%3D-4%7D+%5Catop+%7B%5Cfrac%7B7%7D%7Bx%2B2%7D-%5Cfrac%7B10%7D%7By%7D+%3D+6%7D%7D+%5Cright.+%5C%5C%5C%5C%0Ay+%3D+-4-3x%5C%5C%5C%5C%0A%5Cfrac%7B7%7D%7Bx%2B2%7D-%5Cfrac%7B10%7D%7By%7D+%3D+%5Cfrac%7B7%7D%7Bx%2B2%7D%2B%5Cfrac%7B10%7D%7B4%2B3x%7D+%3D+6%5C%5C%5C%5C%0A7%284%2B3x%29%2B10%28x%2B2%29+%3D+6%28x%2B2%29%284%2B3x%29%5C%5C%0A48%2B31x+%3D+18x%5E2%2B60x%2B48%5C%5C%0A18x%5E2%2B29x+%3D+0%5C%5C%5C%5C%0Ax+%3D+0%3B+y+%3D+-4%5C%5C%0Ax+%3D+-29%2F18%3B+y+%3D+-4%2B29%2F6+%3D+5%2F6)
Два решения
x=0; y = -4
x = -29/18; y = 5/6
3)-----
![\left \{ {{\frac{1}{x}+\frac{11}{y}=2} \atop {\frac{2y+1}{6}+\frac{x+4}{2}=\frac{4}{3}}} \right. \\\\ 2y+1+3(x+4) = 4\cdot2 = 8\\ 2y+3x+ 13 = 8\\ 2y+3x = -5\\ y = (-5-3x)/2\\\\ \frac{1}{x}-\frac{22}{3x+5} = 2\\\\ 3x+5-22x = 2x(3x+5)\\ 5-19x = 6x^2+10x\\ 6x^2+29x-5 = 0\\ D = 841 + 120 = 961\\ x = (-29\pm31)/12\\ x = 1/6; y = -2.75\\ x = -5; y = 5](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B%5Cfrac%7B1%7D%7Bx%7D%2B%5Cfrac%7B11%7D%7By%7D%3D2%7D+%5Catop+%7B%5Cfrac%7B2y%2B1%7D%7B6%7D%2B%5Cfrac%7Bx%2B4%7D%7B2%7D%3D%5Cfrac%7B4%7D%7B3%7D%7D%7D+%5Cright.+%5C%5C%5C%5C%0A2y%2B1%2B3%28x%2B4%29+%3D+4%5Ccdot2+%3D+8%5C%5C%0A2y%2B3x%2B+13+%3D+8%5C%5C%0A2y%2B3x+%3D+-5%5C%5C%0Ay+%3D+%28-5-3x%29%2F2%5C%5C%5C%5C%0A%5Cfrac%7B1%7D%7Bx%7D-%5Cfrac%7B22%7D%7B3x%2B5%7D+%3D+2%5C%5C%5C%5C%0A3x%2B5-22x+%3D+2x%283x%2B5%29%5C%5C%0A5-19x+%3D+6x%5E2%2B10x%5C%5C%0A6x%5E2%2B29x-5+%3D+0%5C%5C%0AD+%3D+841+%2B+120+%3D+961%5C%5C%0Ax+%3D+%28-29%5Cpm31%29%2F12%5C%5C%0Ax+%3D+1%2F6%3B+y+%3D+-2.75%5C%5C%0Ax+%3D+-5%3B+y+%3D+5)
Два решения
x = 1/6; y = -2.75
x = -5; y = 5
пусть во втором мешке уменьшается х кг, тогда в первом 3х кг
и того уравнение
3х+х=24
4х=24
х=6 кг- во втором мешке
тогда в первом з*6=18
Ответ 18 кг в первом мешке, 6 кг во втором мешке
Якщо у нас в тижні 7 днів, то потрібно від тижня відняти 3 доби.
1). 7-3 = 4(доби) - Оля була у бабусі
Відповідь:4 доби