А)(n+1)(2n-3)+(n-1)(3n+1)=2n²-3n+2n-3+3n²+n-3n-1=5n²-3n-4
б)(x-y)(2x-3y)-(3x-y)(2x+y)=2x²-3yx-2xy+3y²-6x²+3xy-2xy-y²=-4x²-4xy+2y²
в)(2a+3)(2a+3)-(2a+1)(2a-1)=4a²+6a+6a+9-4a²-2a+2a-1=12a-8
г)(3c-d)(d+3c)+(4c-d)(c-4d)=3cd+9c²-d²-3cd+4c²-16cd-cd+4d²=13c²+3d²-17cd
из 30 учащихся группы 15 умеют вязать, а 12 шить. Кауим может быть число учащихся, умеющих вязать и шить?
на фото.................................
![cos(x-\frac{5\pi }{6})\geq- \frac{1}{2} \\ \\\frac{-2\pi }{3} +2\pi n \leq x- \frac{5\pi }{6} \leq \frac{2\pi }{3} +2\pi n,n\in Z](https://tex.z-dn.net/?f=cos%28x-%5Cfrac%7B5%5Cpi+%7D%7B6%7D%29%5Cgeq-+%5Cfrac%7B1%7D%7B2%7D+%5C%5C+%5C%5C%5Cfrac%7B-2%5Cpi+%7D%7B3%7D+%2B2%5Cpi+n+%5Cleq+x-+%5Cfrac%7B5%5Cpi+%7D%7B6%7D+%5Cleq+%5Cfrac%7B2%5Cpi+%7D%7B3%7D+%2B2%5Cpi+n%2Cn%5Cin+Z)
Прибавим ко всем частям неравенства
![\frac{5\pi }{6}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Cpi+%7D%7B6%7D)
![\frac{-2\pi }{3}+\frac{5\pi }{6} +2\pi n \leq x\leq \frac{2\pi }{3}+\frac{5\pi }{6}+2\pi n,n\in Z\\ \\\frac{\pi }{6} +2\pi n \leq x\leq \frac{3\pi }{2}+2\pi n,n\in Z](https://tex.z-dn.net/?f=%5Cfrac%7B-2%5Cpi+%7D%7B3%7D%2B%5Cfrac%7B5%5Cpi+%7D%7B6%7D+%2B2%5Cpi+n+%5Cleq+x%5Cleq+%5Cfrac%7B2%5Cpi+%7D%7B3%7D%2B%5Cfrac%7B5%5Cpi+%7D%7B6%7D%2B2%5Cpi+n%2Cn%5Cin+Z%5C%5C+%5C%5C%5Cfrac%7B%5Cpi+%7D%7B6%7D+%2B2%5Cpi+n+%5Cleq+x%5Cleq+%5Cfrac%7B3%5Cpi+%7D%7B2%7D%2B2%5Cpi+n%2Cn%5Cin+Z)
Наименьшее положительное x=![\frac{\pi }{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi+%7D%7B6%7D)
![\frac{-3\pi }{4} +2\pi n \leq \frac{x}{4}-1 \leq \frac{-\pi }{4} +2\pi n,n\in Z\\ \\ 1+\frac{-3\pi }{4} +2\pi n \leq \frac{x}{4} \leq 1+\frac{-\pi }{4} +2\pi n,n\in Z\\ \\4-3\pi+8\pi n \leqx\leq4-\pi+8\pi n, n\in Z](https://tex.z-dn.net/?f=%5Cfrac%7B-3%5Cpi+%7D%7B4%7D+%2B2%5Cpi+n+%5Cleq+%5Cfrac%7Bx%7D%7B4%7D-1+%5Cleq+%5Cfrac%7B-%5Cpi+%7D%7B4%7D+%2B2%5Cpi+n%2Cn%5Cin+Z%5C%5C+%5C%5C+1%2B%5Cfrac%7B-3%5Cpi+%7D%7B4%7D+%2B2%5Cpi+n+%5Cleq+%5Cfrac%7Bx%7D%7B4%7D+%5Cleq+1%2B%5Cfrac%7B-%5Cpi+%7D%7B4%7D+%2B2%5Cpi+n%2Cn%5Cin+Z%5C%5C+%5C%5C4-3%5Cpi%2B8%5Cpi+n+%5Cleqx%5Cleq4-%5Cpi%2B8%5Cpi+n%2C+n%5Cin+Z)
4-3π≈-5,42>-6
4-π≈0,86<2
Значит целые решения, принадлежащие отрезку [-6;2]
-5;-4;-3;-2;-1;0
О т в е т. 6 целых решений
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