Решите уравнения: (даю 24 балла) 1)x²+2(a-b)x-4ab=0 2)56²+ay-a²=0 3)abx²-(a²-b²)x-ab=0 4)2y²-(b-2c)y=bc 5)(m-n)x²-nx-m=0
Решите уравнения: (даю 24 балла)
1)x²+2(a-b)x-4ab=0
2)56²+ay-a²=0
3)abx²-(a²-b²)x-ab=0
4)2y²-(b-2c)y=bc
5)(m-n)x²-nx-m=0
1)x²+2(a-b)x-4ab=0
2)56²+ay-a²=0
3)abx²-(a²-b²)x-ab=0
4)2y²-(b-2c)y=bc
5)(m-n)x²-nx-m=0
1 ответ:
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По свойству арифметической прогрессии:
![cos^2 (\pi x)=-cos( \pi x) \\ cos^2 (\pi x)+cos( \pi x)=0 \\ cos( \pi x)*(cos( \pi x)+1)=0 \\ \\ cos( \pi x)=0 \\ cos( \pi x)=-1 \\ xE[0;2] \\ \\ \pi x= \frac{ \pi }{2} + \pi n,nEZ \\ \pi x= \pi +2 \pi k,kEZ \\ xE[0;2] \\ \\ x= \frac{1}{2} +n,nE Z \\ x=1+2k,kEZ \\ xE[0;2]\\](https://tex.z-dn.net/?f=+cos%5E2+%28%5Cpi+x%29%3D-cos%28+%5Cpi+x%29+%5C%5C++cos%5E2+%28%5Cpi+x%29%2Bcos%28+%5Cpi+x%29%3D0+%5C%5C+cos%28+%5Cpi+x%29%2A%28cos%28+%5Cpi+x%29%2B1%29%3D0+%5C%5C++%5C%5C+cos%28+%5Cpi+x%29%3D0+%5C%5C+cos%28+%5Cpi+x%29%3D-1+%5C%5C+xE%5B0%3B2%5D+%5C%5C++%5C%5C++%5Cpi+x%3D+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B+%5Cpi+n%2CnEZ+%5C%5C++%5Cpi+x%3D+%5Cpi+%2B2+%5Cpi+k%2CkEZ+%5C%5C+xE%5B0%3B2%5D+%5C%5C++%5C%5C+x%3D+%5Cfrac%7B1%7D%7B2%7D+%2Bn%2CnE+Z+%5C%5C+x%3D1%2B2k%2CkEZ+%5C%5C+xE%5B0%3B2%5D%5C%5C)
x ∈ {1/2; 1; 3/2}
Ответ: 1/2 + 1 + 3/2 = 3.