Х^2(Х-у)+х(Х-у)=(Х-у)(х^2+Х)
![\frac{2sin^2x-sinx}{2cosx- \sqrt{3} } =0 \\ \\ \begin{cases} 2sin^2x-sinx=0 \\ 2cosx- \sqrt{3} \neq 0 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} sinx(2sinx-1)=0 \\ cosx \neq \frac{\sqrt{3}}{2} \end{cases} =\ \textgreater \ \\ \begin{cases} \left[ \begin{matrix} sinx=0\\ sinx= \frac{1}{2} \end{matrix}\right \\ cosx \neq \frac{\sqrt{3}}{2} \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} \left[ \begin{matrix} x= \pi k\\ x= \frac{ \pi }{6}+2 \pi k\\ x= \frac{ 5 \pi }{6}+2 \pi k \end{matrix}\right \\ x \neq \pm\frac{ \pi }{6}+2 \pi k \end{cases}](https://tex.z-dn.net/?f=+%5Cfrac%7B2sin%5E2x-sinx%7D%7B2cosx-+%5Csqrt%7B3%7D+%7D+%3D0+%5C%5C+%5C%5C+%5Cbegin%7Bcases%7D+2sin%5E2x-sinx%3D0+%5C%5C+2cosx-+%5Csqrt%7B3%7D+%5Cneq+0+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5Cbegin%7Bcases%7D+sinx%282sinx-1%29%3D0+%5C%5C+cosx+%5Cneq++%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D++%5Cend%7Bcases%7D+%3D%5C+%5Ctextgreater+%5C++%5C%5C%0A%5Cbegin%7Bcases%7D+%5Cleft%5B+%5Cbegin%7Bmatrix%7D+sinx%3D0%5C%5C+sinx%3D+%5Cfrac%7B1%7D%7B2%7D++%5Cend%7Bmatrix%7D%5Cright+%5C%5C+cosx+%5Cneq++%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D++%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%0A%5Cbegin%7Bcases%7D+%5Cleft%5B+%5Cbegin%7Bmatrix%7D+x%3D+%5Cpi+k%5C%5C+x%3D+%5Cfrac%7B+%5Cpi+%7D%7B6%7D%2B2+%5Cpi+k%5C%5C+x%3D+%5Cfrac%7B+5+%5Cpi+%7D%7B6%7D%2B2+%5Cpi+k+%5Cend%7Bmatrix%7D%5Cright+%5C%5C+x+%5Cneq+%5Cpm%5Cfrac%7B+%5Cpi+%7D%7B6%7D%2B2+%5Cpi+k+%5Cend%7Bcases%7D)
![=\ \textgreater \ x= \pi k;\ x = \frac{5\pi }{6}+2 \pi k,\ k \in Z](https://tex.z-dn.net/?f=%3D%5C+%5Ctextgreater+%5C++x%3D+%5Cpi++k%3B%5C+x+%3D+%5Cfrac%7B5%5Cpi+%7D%7B6%7D%2B2+%5Cpi+k%2C%5C+k+%5Cin+Z)
Символ
![\Big[](https://tex.z-dn.net/?f=%5CBig%5B)
- знак совокупности - заменяет слово "ИЛИ"
Примем за Х - собственную скорость катера, тогда (Х+2) км/ч - скорость по течению, и (Х-2) - скорость против течения
16/(Х+2)+12/(Х-2)=5
16(X-2)/((x-2)(x+2)+12(x+2)/((x-2)(x+2)=5
16x-32+12x+24=5(X-2)(X+2)
28x-8=5(x^2-4)
5x^2-20-28x+8=0
5x^2-28x-12=0
D=784+240=32^2
X1=(28-32)/10=-0,4 не подходит
X2=(28+32)/10=6 км/ч
Ответ: 6км/ч собственная скорость катера
.........Держите )..........