2 в 2+7 в 3 не = 14 т.к.
2*2=4. 7*7*7=343.
4+343=347.
Обычный пример
Применены свойства тригонометрических функций
![tg(4x+\frac{\pi}{3})<2\\\\-\frac{\pi}{2}+\pi n<4x+\frac{\pi}{3}<arctg2+\pi n](https://tex.z-dn.net/?f=tg%284x%2B%5Cfrac%7B%5Cpi%7D%7B3%7D%29%3C2%5C%5C%5C%5C-%5Cfrac%7B%5Cpi%7D%7B2%7D%2B%5Cpi+n%3C4x%2B%5Cfrac%7B%5Cpi%7D%7B3%7D%3Carctg2%2B%5Cpi%C2%A0n)
Вычтем из всех частей неравенства число
![\frac{\pi}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%7D%7B3%7D)
.
![-\frac{5\pi}{6}+\pi n<4x<-\frac{\pi}{3}+arctg2+\pi n\; |:4\\\\-\frac{5\pi}{24}+\frac{\pi n}{4}<x<-\frac{\pi}{12}+\frac{1}{4}arctg2+\frac{\pi n}{4},n\in Z](https://tex.z-dn.net/?f=-%5Cfrac%7B5%5Cpi%7D%7B6%7D%2B%5Cpi+n%3C4x%3C-%5Cfrac%7B%5Cpi%7D%7B3%7D%2Barctg2%2B%5Cpi+n%5C%3B+%7C%3A4%5C%5C%5C%5C-%5Cfrac%7B5%5Cpi%7D%7B24%7D%2B%5Cfrac%7B%5Cpi+n%7D%7B4%7D%3Cx%3C-%5Cfrac%7B%5Cpi%7D%7B12%7D%2B%5Cfrac%7B1%7D%7B4%7Darctg2%2B%5Cfrac%7B%5Cpi+n%7D%7B4%7D%2Cn%5Cin+Z)
69² = (70 - 1)² = 70² - 2 · 70 · 1 + 1² = 4900 - 140 + 1 = 4761
91² = (90 + 1)² = 90² + 2 · 90 · 1 + 1² = 8100 + 180 + 1 = 8281
52² = (50 + 2)² = 50² + 2 · 50 · 2 + 2² = 2500 + 200 + 4 = 2704
97² = (100 - 3)² = 100² - 2 · 100 · 3 + 3² = 10000 - 600 + 9 = 9409
299² = (300 -1)² = 300² - 2 · 300 · 1 + 1² = 90000 - 600 + 1 = 89401
10,2² = (10 + 0,2)² = 10² + 2 · 10 · 0,2 + 0,2² = 100 + 4 + 0,04 = 104,04