Х+1/2*х-20=1/4х
1,5х-0.25х=20
1.25х=20
х=16
Ответ:х=16.
дело в том,что tg(arctg a)=a,анлогично получается:
-1/корень из3+пи/4+ пи/2+ 1/корень из3,
приводим подобные , получается 3пи/4,или 135 градусов)
![x+y=\pi => x=\pi-y](https://tex.z-dn.net/?f=x%2By%3D%5Cpi+%3D%3E+x%3D%5Cpi-y)
![sin(\pi-y)+siny=1](https://tex.z-dn.net/?f=sin%28%5Cpi-y%29%2Bsiny%3D1)
![siny+siny=1](https://tex.z-dn.net/?f=siny%2Bsiny%3D1)
![y=(-1)^k\frac{\pi}{6}+\pi k,k \in Z](https://tex.z-dn.net/?f=y%3D%28-1%29%5Ek%5Cfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi+k%2Ck+%5Cin+Z)
Значит
![x=(-1)^{k-1}\frac{\pi}{6}-\pi (k-1),k \in Z](https://tex.z-dn.net/?f=x%3D%28-1%29%5E%7Bk-1%7D%5Cfrac%7B%5Cpi%7D%7B6%7D-%5Cpi+%28k-1%29%2Ck+%5Cin+Z)
Сложим оба равенства для проверки:
![x+y=(-1)^k\frac{\pi}{6}+\pi k+(-1)^{k-1}\frac{\pi}{6}-\pi (k-1)=\frac{\pi}{6}((-1)^k+(-1)^{k-1})+\pi k-\pi k+\pi=\frac{\pi}{6}*0+\pi=\pi](https://tex.z-dn.net/?f=x%2By%3D%28-1%29%5Ek%5Cfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi+k%2B%28-1%29%5E%7Bk-1%7D%5Cfrac%7B%5Cpi%7D%7B6%7D-%5Cpi+%28k-1%29%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%28%28-1%29%5Ek%2B%28-1%29%5E%7Bk-1%7D%29%2B%5Cpi+k-%5Cpi+k%2B%5Cpi%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%2A0%2B%5Cpi%3D%5Cpi)
Система уравнений
х + y = 45
2•0,5x = 1/5y
Решение
х = 1/5y = 0,2y
0,2y + y = 45
1,2y = 45
y = 37,5
x = 0,2•37,5 = 7,5
Ответ числа 7,5 и 37,5