1)6x(x-y)-8(x-y)=(6x-8)(x-y)
2)a(a-b)-5(a-b)=(a-5)(a-b)
3)b(b+c)+a(b+c)=(b+a)(b+c)
4)xy(3-(x^2)*(y^2))-2(3-(x^2)*(y^2))=(xy-2)*(3-(x^2)(y^2)
![2sin^2x - 5sinxcosx + 5cos^2x = 1](https://tex.z-dn.net/?f=2sin%5E2x+-+5sinxcosx+%2B+5cos%5E2x+%3D+1+)
![2sin^2x - 5sinxcosx + 5cos^2x = Sin^2x+Cos^2x](https://tex.z-dn.net/?f=2sin%5E2x+-+5sinxcosx+%2B+5cos%5E2x+%3D+Sin%5E2x%2BCos%5E2x)
![Sin^2x - 5sinxcosx + 4cos^2x = 0](https://tex.z-dn.net/?f=Sin%5E2x+-+5sinxcosx+%2B+4cos%5E2x+%3D+0)
Разделим правую и левую части на sinxcosx (sinxcosx=0 не может быть решением)
![\frac{Sinx}{Cosx} - 5 + 4\frac{Cosx}{Sinx} = 0](https://tex.z-dn.net/?f=%5Cfrac%7BSinx%7D%7BCosx%7D+-+5+%2B+4%5Cfrac%7BCosx%7D%7BSinx%7D+%3D+0)
![tgx - 5 + 4\frac{1}{tgx} = 0](https://tex.z-dn.net/?f=tgx+-+5+%2B+4%5Cfrac%7B1%7D%7Btgx%7D+%3D+0)
Сделаем замену tgx=y
![y - 5 + 4\frac{1}{y} = 0](https://tex.z-dn.net/?f=y+-+5+%2B+4%5Cfrac%7B1%7D%7By%7D+%3D+0)
Домножим на y
![y^2 - 5y + 4 = 0](https://tex.z-dn.net/?f=y%5E2+-+5y+%2B+4+%3D+0)
По Т.Виета: ![y_1=1 \ \ \ \ \ \ y_2=4](https://tex.z-dn.net/?f=y_1%3D1+%5C+%5C+%5C+%5C+%5C+%5C+y_2%3D4)
Обратная замена
![tgx=1 \ \ \ \ \ \ \ tgx=4](https://tex.z-dn.net/?f=tgx%3D1+%5C+%5C+%5C+%5C+%5C+%5C+%5C+tgx%3D4)
![x=\frac{\pi}{4}+\pi n \ \ \ \ \ \ \ \ x=arctg(4)+\pi n](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cpi+n+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+x%3Darctg%284%29%2B%5Cpi+n)
Дискриминант = 625. Хорошо перемножай.
25x^2+10x+1-15x-3-4=0
25x^2-5x-6=0
D= 25-4*25*(-6)=25+600=625
-36(6x+1)=9(4 -2x)
-216-36=36-18х
-216х+18х=36+36
-198х=72
х= -4/17
нам тоже на днях такое уравнение задавали:)
4*3000=12000
12000=100%
x=95%
x=95*12000/100=11400
Ответ: 11400 руб.