Sin (pi/12 + 2pi/3) = sin ( (pi+8pi) /12) = sin 9pi/12 = sin 3pi/4 = √2/2
1) Y^3 * V 4Y^2 = Y^3 * 2Y = 2Y^4
2) 7A * V ( 16 \ A^2) = 7A * 4 \ A = 7A * 4A^(-1) = 28 A^ ( 1 - 1) = 28 A^0 = 28
Вангую, что многочлен, представленный в числителе, делится одновременно на три двучлена, нарисованные в примерах под а, б и в соответственно. доказательство моего предположения:
![(x+3)(x+1)(x-4)=(x^2+4x+3)(x-4)=x^3-13x-12](https://tex.z-dn.net/?f=%28x%2B3%29%28x%2B1%29%28x-4%29%3D%28x%5E2%2B4x%2B3%29%28x-4%29%3Dx%5E3-13x-12)
итак, начинаем:
а)
![\cfrac{(x+3)(x+1)(x-4)}{x+1}=(x+3)(x-4)=x^2-x-12](https://tex.z-dn.net/?f=%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7Bx%2B1%7D%3D%28x%2B3%29%28x-4%29%3Dx%5E2-x-12)
б)
![\cfrac{(x+3)(x+1)(x-4)}{x+3}=(x+1)(x-4)=x^2-3x-4](https://tex.z-dn.net/?f=%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7Bx%2B3%7D%3D%28x%2B1%29%28x-4%29%3Dx%5E2-3x-4)
в)
![\cfrac{(x+3)(x+1)(x-4)}{x-4}=(x+3)(x+1)=x^2+4x+3](https://tex.z-dn.net/?f=%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7Bx-4%7D%3D%28x%2B3%29%28x%2B1%29%3Dx%5E2%2B4x%2B3)
г)
![\cfrac{(x+3)(x+1)(x-4)}{x^2-x-12}=\cfrac{(x+3)(x+1)(x-4)}{(x+3)(x-4)}=x+1](https://tex.z-dn.net/?f=%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7Bx%5E2-x-12%7D%3D%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7B%28x%2B3%29%28x-4%29%7D%3Dx%2B1)
д)
![\cfrac{(x+3)(x+1)(x-4)}{x^2-3x-4}=\cfrac{(x+3)(x+1)(x-4)}{(x+1)(x-4)}=x+3](https://tex.z-dn.net/?f=%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7Bx%5E2-3x-4%7D%3D%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7B%28x%2B1%29%28x-4%29%7D%3Dx%2B3)
е)
![\cfrac{(x+3)(x+1)(x-4)}{x^2+4x+3}=\cfrac{(x+3)(x+1)(x-4)}{(x+3)(x+1)}=x-4](https://tex.z-dn.net/?f=%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7Bx%5E2%2B4x%2B3%7D%3D%5Ccfrac%7B%28x%2B3%29%28x%2B1%29%28x-4%29%7D%7B%28x%2B3%29%28x%2B1%29%7D%3Dx-4)
400.000-100%
х-13%
решаем пропорцию:
100х=5.200.000
х=52.000