1. n! / (n-1)! = (1 * 2 * .... * (n-1) * n) / (<span>1 * 2 * .... * (n-1)) = n
2. по аналогии с первым
</span>Если k - натуральное число, то
(2K+1)! / (2k-1)! = (3 * 5 * ... * (2k-1) * (2k +1)) / (1 * 3 * 5 * ... * (2k - 1) = 3(2k+1) = 6k +3
1)
![\dfrac{x+2}{x^2-2x} -\dfrac{x}{x-2} =\dfrac{3}{x}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bx%2B2%7D%7Bx%5E2-2x%7D%20-%5Cdfrac%7Bx%7D%7Bx-2%7D%20%3D%5Cdfrac%7B3%7D%7Bx%7D%20%20)
ОДЗ:
![x\neq 2\\ x\neq 0\\ \\ x+2-x^2-3x+6=0\\ x^2+2x-8=0\\ \frac{D}{4}=1+8=9=3^2\\ x_1=-1+3=2 \notin ODZ\\ x_2=-1-3=-4](https://tex.z-dn.net/?f=%20x%5Cneq%202%5C%5C%20x%5Cneq%200%5C%5C%20%5C%5C%20x%2B2-x%5E2-3x%2B6%3D0%5C%5C%20x%5E2%2B2x-8%3D0%5C%5C%20%5Cfrac%7BD%7D%7B4%7D%3D1%2B8%3D9%3D3%5E2%5C%5C%20%20x_1%3D-1%2B3%3D2%20%5Cnotin%20ODZ%5C%5C%20x_2%3D-1-3%3D-4%20)
Ответ: -4
2)
![\left\{\begin{array}{I} x^2-xy=-2 \\ y^2-xy=3 \end{array}}](https://tex.z-dn.net/?f=%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D%20x%5E2-xy%3D-2%20%20%5C%5C%20y%5E2-xy%3D3%20%5Cend%7Barray%7D%7D%20)
разделим первое уравнение на второе
![\dfrac{x(x-y)}{y(y-x)}=-\dfrac{2}{3} \ \Rightarrow \ -\dfrac{x}{y}=-\dfrac{2}{3} \ \Rightarrow \ 3x=2y \ \Rightarrow \ y= \dfrac{3x}{2}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bx%28x-y%29%7D%7By%28y-x%29%7D%3D-%5Cdfrac%7B2%7D%7B3%7D%20%5C%20%5CRightarrow%20%5C%20-%5Cdfrac%7Bx%7D%7By%7D%3D-%5Cdfrac%7B2%7D%7B3%7D%20%5C%20%5CRightarrow%20%5C%203x%3D2y%20%5C%20%5CRightarrow%20%5C%20y%3D%20%5Cdfrac%7B3x%7D%7B2%7D%20%20%20%20%20)
выполняем подстановку
![x^2-x\cdot\dfrac{3x}{2}=-2\\ x^2-1,5x^2=-2\\ -0,5x^2=-2\\ x^2=4\\ x=\pm 2 \ \Rightarrow \ y=\dfrac{3 \cdot \pm2}{2}=\pm3](https://tex.z-dn.net/?f=%20x%5E2-x%5Ccdot%5Cdfrac%7B3x%7D%7B2%7D%3D-2%5C%5C%20%20x%5E2-1%2C5x%5E2%3D-2%5C%5C%20-0%2C5x%5E2%3D-2%5C%5C%20x%5E2%3D4%5C%5C%20x%3D%5Cpm%202%20%5C%20%5CRightarrow%20%20%5C%20y%3D%5Cdfrac%7B3%20%5Ccdot%20%5Cpm2%7D%7B2%7D%3D%5Cpm3%20%20)
Ответ: (-2; -3), (2; 3)
Не согласен...
Вот правильное решение:
7√25 (cos5π/8)^2-7√2(sin(5/8π)^2=7√2((1+cos(10/8π))/2-(1-cos(10/8π))/2)= =7√2(1+cos10π/8-1+cos10π/8)/2=7√2(2*cos5√π/4)/2=7√2*cos(π+π/4)= = -7√2cosπ/4 =-7√2*1/√2=-7. 5cos37°/sin53°=5cos(90°-53° ) /sin53°=5sin53° /sin53° =5. 24sin298° /sin62°=24sin(360°-62 ° )/sin62°= -24sin62°/sin62°=-24. 15tg15°*tg285°=15tg15°*tg(270°+15°)=15tg15°*ctg15°= 15*1=15. 18√6cos(17/4π*cosπ/6=18√6cos(4π+π/4)cosπ/6 =18√6cosπ/4cosπ/6=18√6*√2/2*√3/2=18*6/4=9*3=27.