Решим это методом мат. индукции
1) Базис индукции
n=1
![(7^2-5^2)\,\,\vdots\,\,24\\ 24\,\,\vdots\,\,24](https://tex.z-dn.net/?f=%287%5E2-5%5E2%29%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24%5C%5C+24%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24)
- Выполняется
2) Допустим что при n=k
![(7^{2k}-5^{2k})\,\,\vdots\,\,24](https://tex.z-dn.net/?f=%287%5E%7B2k%7D-5%5E%7B2k%7D%29%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24)
тоже выполняется
3) Индукционный переход
n=k+1
![(7^{2k+2}-5^{2k+2})\,\,\vdots\,\,24\\ (49\cdot7^{2k}-25\cdot5^{2k})\,\,\vdots\,\,24\\ ((24+25)\cdot7^{2k}-25\cdot5^{2k})\,\,\vdots\,\,24](https://tex.z-dn.net/?f=%287%5E%7B2k%2B2%7D-5%5E%7B2k%2B2%7D%29%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24%5C%5C+%2849%5Ccdot7%5E%7B2k%7D-25%5Ccdot5%5E%7B2k%7D%29%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24%5C%5C+%28%2824%2B25%29%5Ccdot7%5E%7B2k%7D-25%5Ccdot5%5E%7B2k%7D%29%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24)
![(25(7^{2k}-5^{2k})+24\cdot7^{2k})\,\,\vdots\,\,24\\ \,\,\,\,\,\,.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\vdots\,\,24\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\vdots\,\,24](https://tex.z-dn.net/?f=%2825%287%5E%7B2k%7D-5%5E%7B2k%7D%29%2B24%5Ccdot7%5E%7B2k%7D%29%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24%5C%5C+%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C.%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5Cvdots%5C%2C%5C%2C24)
Что и требовалось доказать
1)4х→-7-5
4х→-12
х→-3
(-3;+бесконечности)
2)-3хбольше либо равно -9
х меньше либо равно 3
(-бесконечности; 3]
3)
-6х больше либо равно -23-13
-6х больше либо равно -36
х меньше либо равно 6
(-бесконечности ;6]
4)
-9х→16-5
-9х→11
х←- 11\9
(-бесконечности;-11\9)
5)-4х меньше либо равно -2
х больше либо равно 0.5
[0.5;+бесконечности)
5*3+6у=15;
15+6у=15
6у=0
у=0.