Ответ: a) π/4 + πn, n ∈ Z, arctg(-2/3) + \pi k, k \in Z
b) 5π/4, arctg(-2/3) + π/2, arctg(-2/3) + 3π/2
![(1): \ 1 - 9\log_{8}^{2}x \ge 0 \\ \\ 9\log_{8}^{2}x \le 1 \\ \\ \log_{8}^{2}x \le \dfrac{1}{9} \\ \\ |\log_{8}x| \le \dfrac{1}{3} \\ \\ -\dfrac{1}{3} \le \log_{8}x \le \dfrac{1}{3} \\ \\ \log_{8}8^{-\frac{1}{3}} \le \log_{8}x \le \log_{8}8^{\frac{1}{3}} \\ \\ 8^{-\frac{1}{3}} \le x \le 8^{\frac{1}{3}} \\ \\ \dfrac{1}{2} \le x \le 2 \ ; \ x \in [\dfrac{1}{2};2]](https://tex.z-dn.net/?f=+%281%29%3A+%5C+1+-+9%5Clog_%7B8%7D%5E%7B2%7Dx+%5Cge+0+%5C%5C+%5C%5C+9%5Clog_%7B8%7D%5E%7B2%7Dx+%5Cle+1+%5C%5C+%5C%5C+%5Clog_%7B8%7D%5E%7B2%7Dx+%5Cle+%5Cdfrac%7B1%7D%7B9%7D+%5C%5C+%5C%5C+%7C%5Clog_%7B8%7Dx%7C+%5Cle+%5Cdfrac%7B1%7D%7B3%7D+%5C%5C+%5C%5C+-%5Cdfrac%7B1%7D%7B3%7D+%5Cle+%5Clog_%7B8%7Dx+%5Cle+%5Cdfrac%7B1%7D%7B3%7D+%5C%5C+%5C%5C+%5Clog_%7B8%7D8%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D+%5Cle+%5Clog_%7B8%7Dx+%5Cle+%5Clog_%7B8%7D8%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D+%5C%5C+%5C%5C+8%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D+%5Cle+x+%5Cle+8%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D+%5C%5C+%5C%5C+%5Cdfrac%7B1%7D%7B2%7D+%5Cle+x+%5Cle+2+%5C+%3B+%5C+x+%5Cin+%5B%5Cdfrac%7B1%7D%7B2%7D%3B2%5D+++)
![x \in [\dfrac{1}{2} ;2]](https://tex.z-dn.net/?f=+x+%5Cin+%5B%5Cdfrac%7B1%7D%7B2%7D+%3B2%5D+)
Решим уравнение:
ИЛИ
![-\dfrac{24}{25} < \log_{2}x < 0 \\ \\ \log_{2}2^{-\frac{24}{25}} < \log_{2}x < \log_{2}2^{0} \\ \\ 2^{-\frac{24}{25}}< x < 1 \ ; \ x \in (\dfrac{1}{\sqrt[25]{2^{24}}}; 1)](https://tex.z-dn.net/?f=+-%5Cdfrac%7B24%7D%7B25%7D+%3C+%5Clog_%7B2%7Dx+%3C+0+%5C%5C+%5C%5C+%5Clog_%7B2%7D2%5E%7B-%5Cfrac%7B24%7D%7B25%7D%7D+%3C+%5Clog_%7B2%7Dx+%3C+%5Clog_%7B2%7D2%5E%7B0%7D+%5C%5C+%5C%5C+2%5E%7B-%5Cfrac%7B24%7D%7B25%7D%7D%3C+x+%3C+1+%5C+%3B+%5C+x+%5Cin+%28%5Cdfrac%7B1%7D%7B%5Csqrt%5B25%5D%7B2%5E%7B24%7D%7D%7D%3B+1%29++++++)
![(3): \ 1 + \dfrac{4}{3}\log_{2}x \ge 0 \\ \\ \log_{2}x \ge \log_{2}2^{-\frac{3}{4}} \\ \\ x \ge 2^{-\frac{3}{4}} \ ; \ x \in [\dfrac{1}{\sqrt[4]{2^{3}}}; +\infty)](https://tex.z-dn.net/?f=+%283%29%3A+%5C+1+%2B+%5Cdfrac%7B4%7D%7B3%7D%5Clog_%7B2%7Dx+%5Cge+0+%5C%5C+%5C%5C+%5Clog_%7B2%7Dx+%5Cge+%5Clog_%7B2%7D2%5E%7B-%5Cfrac%7B3%7D%7B4%7D%7D+%5C%5C+%5C%5C+x+%5Cge+2%5E%7B-%5Cfrac%7B3%7D%7B4%7D%7D+%5C+%3B+%5C+x+%5Cin+%5B%5Cdfrac%7B1%7D%7B%5Csqrt%5B4%5D%7B2%5E%7B3%7D%7D%7D%3B+%2B%5Cinfty%29++++)
Пересечём (2) и (3):
![x \in [\dfrac{1}{\sqrt[4]{2^{3}}};1)](https://tex.z-dn.net/?f=+x+%5Cin+%5B%5Cdfrac%7B1%7D%7B%5Csqrt%5B4%5D%7B2%5E%7B3%7D%7D%7D%3B1%29++++)
![(3): \ x \in R \\ \\ (4): \ 1 + \dfrac{4}{3}\log_{2}x \ \textless \ 0 \\ \\ \log_{2}x \ \textless \ - \dfrac{3}{4} \\ \\ x \ \textless \ \dfrac{1}{ \sqrt[4]{2^{3}}}](https://tex.z-dn.net/?f=%283%29%3A+%5C+x+%5Cin+R+%5C%5C+%5C%5C+%284%29%3A+%5C+1+%2B++%5Cdfrac%7B4%7D%7B3%7D%5Clog_%7B2%7Dx+%5C+%5Ctextless+%5C++0+%5C%5C+%5C%5C+%5Clog_%7B2%7Dx+%5C+%5Ctextless+%5C++-+%5Cdfrac%7B3%7D%7B4%7D+%5C%5C+%5C%5C+x+%5C+%5Ctextless+%5C+++%5Cdfrac%7B1%7D%7B+%5Csqrt%5B4%5D%7B2%5E%7B3%7D%7D%7D+)
Пересечём (2) и (3) с (3) и (4):
Учтём ОДЗ (рисунок 3):
Ответ: x ∈ [1/2; 1)
Sn = a1+an\2 *n
S29 = (18,7 - 19,6\2) *29
S29= -13,05
1) 343^(2㏒₄₉2)=(7³)^(2㏒₇²2)=7^(3*2*1/2㏒₇2)=7^㏒₇ 2³=2³=8
2) 4^(2㏒₃₂10)=(2²)^(2㏒₂⁵10)=2^(4*1/5㏒₂10)=2^(4/5 ㏒₂10)=10^(⁴/₅)
3) √5=5^(¹/₂)
(5^(¹/₂))^2㏒₅3=5^㏒₅3=3
4) 9^2㏒₂₇√5 = (3²)^2㏒₂₇√5 = 3^4㏒₃³ 5^(¹/₂)= 3^4*1/2*1/3*㏒₃5 =
=3^2/3㏒₃5=5^(2/3) =∛25
5) (1/27)^㏒₁/₉4= ((1/3)³)^1/2㏒₁/₃4=(1/3)^(3*1/2*㏒₁/₃4)=(1/3)^㏒₁/₃4^(³/₂)=
= 4^³/₂=√4³=√64=8
6) 4^㏒₈125=(2²)^㏒₂³5³=2^2㏒₂³5³=2^2㏒₂5=2^㏒₂5²= 25
1) x^2+y^2+2xy=49
x^2+y^2=25
2xy=49-25=24
xy=12
x+y=-7
применяя обратную теорему Виета имеемпары решенийэ
(-3;-4) и (-4;-3)
x+y=10
x^2+y^2=148
2xy=-48
x+y=10
xy=-24
(12;-2) (-2;12)
