![2Cos2x+4\sqrt{3}Cosx-7=0\\\\2(2Cos^{2}x-1)+4\sqrt{3}Cosx-7=0\\\\4Cos^{2}x-2+4\sqrt{3}Cosx-7=0\\\\4Cos^{2}x+4\sqrt{3}Cosx-9=0\\\\Cosx=m,-1 \leq m \leq 1 \\\\4m^{2} +4\sqrt{3}m-9=0](https://tex.z-dn.net/?f=2Cos2x%2B4%5Csqrt%7B3%7DCosx-7%3D0%5C%5C%5C%5C2%282Cos%5E%7B2%7Dx-1%29%2B4%5Csqrt%7B3%7DCosx-7%3D0%5C%5C%5C%5C4Cos%5E%7B2%7Dx-2%2B4%5Csqrt%7B3%7DCosx-7%3D0%5C%5C%5C%5C4Cos%5E%7B2%7Dx%2B4%5Csqrt%7B3%7DCosx-9%3D0%5C%5C%5C%5CCosx%3Dm%2C-1%20%5Cleq%20m%20%5Cleq%201%20%5C%5C%5C%5C4m%5E%7B2%7D%20%2B4%5Csqrt%7B3%7Dm-9%3D0)
![D=(4\sqrt{3})^{2}-4*4*(-9)=48+144=192=(8\sqrt{3})^{2}\\\\m_{1} =\frac{-4\sqrt{3}+8\sqrt{3}}{8} =\frac{4\sqrt{3} }{8} =\frac{\sqrt{3} }{2}\\\\m_{2}=\frac{-4\sqrt{3}-8\sqrt{3}}{8}=-\frac{12\sqrt{3} }{8}=-\frac{3\sqrt{3} }{2}<-1](https://tex.z-dn.net/?f=D%3D%284%5Csqrt%7B3%7D%29%5E%7B2%7D-4%2A4%2A%28-9%29%3D48%2B144%3D192%3D%288%5Csqrt%7B3%7D%29%5E%7B2%7D%5C%5C%5C%5Cm_%7B1%7D%20%3D%5Cfrac%7B-4%5Csqrt%7B3%7D%2B8%5Csqrt%7B3%7D%7D%7B8%7D%20%3D%5Cfrac%7B4%5Csqrt%7B3%7D%20%7D%7B8%7D%20%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%5C%5C%5C%5Cm_%7B2%7D%3D%5Cfrac%7B-4%5Csqrt%7B3%7D-8%5Csqrt%7B3%7D%7D%7B8%7D%3D-%5Cfrac%7B12%5Csqrt%7B3%7D%20%7D%7B8%7D%3D-%5Cfrac%7B3%5Csqrt%7B3%7D%20%7D%7B2%7D%3C-1)
Второй корень не подходит
![Cosx=\frac{\sqrt{3} }{2}\\\\x=\pm arcCos\frac{\sqrt{3} }{2}+2\pi n,n\in z\\\\x=\pm \frac{\pi }{6}+2\pi n,n\in z](https://tex.z-dn.net/?f=Cosx%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%5C%5C%5C%5Cx%3D%5Cpm%20arcCos%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%2B2%5Cpi%20n%2Cn%5Cin%20z%5C%5C%5C%5Cx%3D%5Cpm%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%2B2%5Cpi%20n%2Cn%5Cin%20z)
0,027a⁹+64b³=(0,3a³)³+(4b)³=(0,3a³+4b)(0,09a⁶+1,2a³b+16b²).
Решение смотри на фотографии
X² +xy -x² -2xy = -xy = -(√12 *√3) = -(√(12*3) = -√36 = -6
Натуральные числа составляют арифметическую прогрессию с разностью 1.
сумма первых 100
(1+100)*100/2=101*50=5050