![49^x-6*7^x-7=0 \\ \\ 7^{2x}-6*7^x-7=0](https://tex.z-dn.net/?f=49%5Ex-6%2A7%5Ex-7%3D0%20%20%5C%5C%20%20%5C%5C%207%5E%7B2x%7D-6%2A7%5Ex-7%3D0)
Пусть
![t = 7^x](https://tex.z-dn.net/?f=t%20%3D%207%5Ex)
![t^{2}-6t-7=0 \\ \\ t_1 =7;](https://tex.z-dn.net/?f=t%5E%7B2%7D-6t-7%3D0%20%20%5C%5C%20%20%5C%5C%20t_1%20%3D7%3B%20)
![t_2 = -1](https://tex.z-dn.net/?f=t_2%20%3D%20-1)
- лишний корень, тогда
![7 = 7^x \\ \\ x = 1](https://tex.z-dn.net/?f=7%20%3D%207%5Ex%20%20%5C%5C%20%20%5C%5C%20x%20%3D%201)
Ответ: х = 1
![2) \ (\frac{1}{5})^ {2x^2-3x} \geq 5^{-x-2}](https://tex.z-dn.net/?f=2%29%20%5C%20%28%5Cfrac%7B1%7D%7B5%7D%29%5E%20%7B2x%5E2-3x%7D%20%20%5Cgeq%205%5E%7B-x-2%7D%20)
![5^ {-2x^2+3x} \geq 5^{-x-2} \\ \\ {-2x^2+3x} \geq {-x-2} \\ \\ {-2x^2+4x+2} \geq 0](https://tex.z-dn.net/?f=5%5E%20%7B-2x%5E2%2B3x%7D%20%20%5Cgeq%20%205%5E%7B-x-2%7D%20%20%5C%5C%20%20%5C%5C%20%7B-2x%5E2%2B3x%7D%20%20%5Cgeq%20%7B-x-2%7D%20%20%5C%5C%20%20%5C%5C%20%7B-2x%5E2%2B4x%2B2%7D%20%20%5Cgeq%200)
Корни уравнения
![x_{1} = 1- \sqrt{2}; \ x_{2} = 1+ \sqrt{2}](https://tex.z-dn.net/?f=%20x_%7B1%7D%20%3D%201-%20%5Csqrt%7B2%7D%3B%20%5C%20%20x_%7B2%7D%20%3D%201%2B%20%5Csqrt%7B2%7D)
<span>Наносим найденные точки на числовую ось и вычисляем знаки на каждом интервале
</span>
![1- \sqrt{2} \leq x \leq 1+ \sqrt{2}](https://tex.z-dn.net/?f=1-%20%5Csqrt%7B2%7D%20%20%20%5Cleq%20x%20%20%5Cleq%201%2B%20%5Csqrt%7B2%7D%20)
Ответ:
![x \in [1- \sqrt{2}; \ 1+ \sqrt{2}]](https://tex.z-dn.net/?f=x%20%5Cin%20%5B1-%20%5Csqrt%7B2%7D%3B%20%5C%201%2B%20%5Csqrt%7B2%7D%5D%20)
A3=43
a11=11
a14 - ?
---------------
a11=a3+d(11-3)
11=43+8d
8d=-32
d=-4
a14=a11+3d
a14=11-12
a14=-1
12+2x≤14-6x<10 ;l:2
6+x≤7-3x<5
![2*sin(x)-3=0\\\\ 2*sin(x)=3\\\\ sin(x)=\frac{3}{2}\\\\ x\not\in(-\infty;\ +\infty)](https://tex.z-dn.net/?f=2%2Asin%28x%29-3%3D0%5C%5C%5C%5C%0A2%2Asin%28x%29%3D3%5C%5C%5C%5C%0Asin%28x%29%3D%5Cfrac%7B3%7D%7B2%7D%5C%5C%5C%5C%0Ax%5Cnot%5Cin%28-%5Cinfty%3B%5C+%2B%5Cinfty%29)
решений нету, по скольку возможные значения синуса:
![-1 \leq sin(\alpha) \leq 1](https://tex.z-dn.net/?f=-1+%5Cleq+sin%28%5Calpha%29+%5Cleq+1)
--------------------------------
![3*cos^2(x)+1=0\\\\ 3*cos^2(x)=-1\\\\ cos^2(x)=-\frac{1}{3}\\\\ x\not\in(-\infty;\ +\infty)](https://tex.z-dn.net/?f=3%2Acos%5E2%28x%29%2B1%3D0%5C%5C%5C%5C%0A3%2Acos%5E2%28x%29%3D-1%5C%5C%5C%5C%0Acos%5E2%28x%29%3D-%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%0Ax%5Cnot%5Cin%28-%5Cinfty%3B%5C+%2B%5Cinfty%29)
решений нету, по скольку возможные значения квадрата косинуса:
![0 \leq cos^2(\alpha) \leq 1](https://tex.z-dn.net/?f=0+%5Cleq+cos%5E2%28%5Calpha%29+%5Cleq+1)
(x-y)²=x²-2xy+y²
(3a+8b)²=9a²+48ab+64b²
(4a²-5b³)²=16a^4-40a²b³+25b^6
(n-m)(n+m)=n²-m²
(5x+7y)(5x-7y)=25x²-49y²
(3a²-2b²)(3a²+2b²)=9a^4-4b^4
(4x+3)²-24x=16x²+24x+9-24x=16x²+9