14-x=6x-3*(x+7); 14-x=6x-3x-21; -x-6x+3x= -21-14; -4x= -35; x=(-35)/(-4)=8 3/4.
![{x}^{3} - (7 + x) < { - 21x}^{2} - 490 \\ {x}^{3} - (343 + 147x + {21x}^{2} + {x}^{3} ) < { - 21x}^{2} - 490 \\ - 343 - 147x < - 490 \\ - 147x < - 147 \\ x > 1](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B3%7D++-+%287+%2B+x%29+%3C+%7B+-+21x%7D%5E%7B2%7D+-+490+%5C%5C++%7Bx%7D%5E%7B3%7D+++-+%28343+%2B+147x+%2B++%7B21x%7D%5E%7B2%7D++%2B++%7Bx%7D%5E%7B3%7D+%29+%3C++%7B+-+21x%7D%5E%7B2%7D++-+490+%5C%5C++-+343+-+147x+%3C++-+490+%5C%5C++-+++147x+%3C+-+147+%5C%5C+x+%3E+1)
Вот такой ответ получился
1)=(2х - 1 - 5)( 2х -1 +5) = (2х-6)(2х +4)
2) = (а+3 -b+2)(a +3 +b-2)=(a - b +5)(a + b +1)
разложить на множители:
1)= (5а -2b)(25a² +10ab +4b²)
2)=(a² +3b)(a^4 -3a²b + 9b²)
3) = (x³ - a³)(x³ + a³) = (x-a)(x² +ax + a²)(x+a)(x² - ax + a²)
4) = (5a - 2b)( 25a² +10ab + 4b²)
упростить:
1) = х² - 2ху + у² -2ху +2у² + х²= 2х² -4ху +3у²
2) = х² +2ху +у² +х² -4у² + 5х = 2х² - 2ху +у² +5х
Наверное, Вы это имели в виду
![1+\frac{\cot(x)\cot(y)*\cos(x+y)}{\cos x\cos y}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccot%28x%29%5Ccot%28y%29%2A%5Ccos%28x%2By%29%7D%7B%5Ccos+x%5Ccos+y%7D)
По формуле котангенса
![\cot\alpha=\frac{\cos\alpha}{\sin\alpha}](https://tex.z-dn.net/?f=%5Ccot%5Calpha%3D%5Cfrac%7B%5Ccos%5Calpha%7D%7B%5Csin%5Calpha%7D)
![1+\frac{\cot(x)\cot(y)*\cos(x+y)}{\cos x\cos y}=1+\frac{\cos(x)\cos(y)*\cos(x+y)}{\cos x\cos y\sin x\sin y}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccot%28x%29%5Ccot%28y%29%2A%5Ccos%28x%2By%29%7D%7B%5Ccos+x%5Ccos+y%7D%3D1%2B%5Cfrac%7B%5Ccos%28x%29%5Ccos%28y%29%2A%5Ccos%28x%2By%29%7D%7B%5Ccos+x%5Ccos+y%5Csin+x%5Csin+y%7D)
Сокращаем числитель и знаменатель
![1+\frac{\cos(x+y)}{\sin x\sin y}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccos%28x%2By%29%7D%7B%5Csin+x%5Csin+y%7D)
Разложим по формуле косинуса суммы
![1+\frac{\cos(x+y)}{\sin x\sin y}=1+\frac{\cos x\cos y -\sin x\sin y}{\sin x\sin y}](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccos%28x%2By%29%7D%7B%5Csin+x%5Csin+y%7D%3D1%2B%5Cfrac%7B%5Ccos+x%5Ccos+y+-%5Csin+x%5Csin+y%7D%7B%5Csin+x%5Csin+y%7D)
Снова сокращаем насколько возможно
![1+\frac{\cos x\cos y -\sin x\sin y}{\sin x\sin y}=1+\frac{\cos x\cos y}{\sin x\sin y}-1](https://tex.z-dn.net/?f=1%2B%5Cfrac%7B%5Ccos+x%5Ccos+y+-%5Csin+x%5Csin+y%7D%7B%5Csin+x%5Csin+y%7D%3D1%2B%5Cfrac%7B%5Ccos+x%5Ccos+y%7D%7B%5Csin+x%5Csin+y%7D-1)
Снова по формуле котангенса
![\frac{\cos x\cos y}{\sin x\sin y}=\cot x\cot y](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ccos+x%5Ccos+y%7D%7B%5Csin+x%5Csin+y%7D%3D%5Ccot+x%5Ccot+y)