помогите решить задание 4,вариант 1
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Ответил m11m
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a)![7^{3-x} textless frac{1}{49} \
7^{3-x} textless 7^{-2} \
3-x textless -2 \
-x textless -2-3 \
-x textless -5 \
x textgreater 5](https://tex.z-dn.net/?f=7%5E%7B3-x%7D+textless+++frac%7B1%7D%7B49%7D+%5C+%0A7%5E%7B3-x%7D+textless++7%5E%7B-2%7D++%5C+%0A3-x+textless++-2+%5C+%0A-x+textless++-2-3+%5C+%0A-x+textless++-5+%5C+%0Ax+textgreater++5 "7^{3-x} textless frac{1}{49} \
7^{3-x} textless 7^{-2} \
3-x textless -2 \
-x textless -2-3 \
-x textless -5 \
x textgreater 5")
x∈(5; +∞)
Ответ: (5; +∞)
б)![(frac{1}{3})^{x^2-4x-1} textgreater 9^{x-1} \
(3^{-1})^{x^2-4x-1} textgreater (3^2)^{x-1} \
-x^2+4x+1 textgreater 2x-2 \
-x^2+4x-2x+1+2 textgreater 0 \
x^2-2x-3 textless 0 \
x^2-2x-3=0 \
D=4+12=16 \
x_{1}= frac{2-4}{2}=-1 \
x_{2}= frac{2+4}{2}=3 \](https://tex.z-dn.net/?f=+%28frac%7B1%7D%7B3%7D%29%5E%7Bx%5E2-4x-1%7D+textgreater++9%5E%7Bx-1%7D+%5C+%0A%283%5E%7B-1%7D%29%5E%7Bx%5E2-4x-1%7D+textgreater++%283%5E2%29%5E%7Bx-1%7D+%5C+%0A-x%5E2%2B4x%2B1+textgreater++2x-2+%5C+%0A-x%5E2%2B4x-2x%2B1%2B2+textgreater++0+%5C+%0Ax%5E2-2x-3+textless++0+%5C+%0Ax%5E2-2x-3%3D0+%5C+%0AD%3D4%2B12%3D16+%5C+%0Ax_%7B1%7D%3D+frac%7B2-4%7D%7B2%7D%3D-1+%5C+%0Ax_%7B2%7D%3D+frac%7B2%2B4%7D%7B2%7D%3D3+%5C++++ "(frac{1}{3})^{x^2-4x-1} textgreater 9^{x-1} \
(3^{-1})^{x^2-4x-1} textgreater (3^2)^{x-1} \
-x^2+4x+1 textgreater 2x-2 \
-x^2+4x-2x+1+2 textgreater 0 \
x^2-2x-3 textless 0 \
x^2-2x-3=0 \
D=4+12=16 \
x_{1}= frac{2-4}{2}=-1 \
x_{2}= frac{2+4}{2}=3 \")
+ - +
--------- -1 --------- 3 ------------
\\\\\
x∈(-1; 3)
Ответ: (-1; 3)
в)![3^{x}-3^{x-3} textgreater 26 \
3^{x}- frac{3^{x}}{3^3} textgreater 26 \
3^{x}(1- frac{1}{27} ) textgreater 26 \
3^{x}* frac{26}{27} textgreater 26 \
3^{x} textgreater 26* frac{27}{26} \
3^{x} textgreater 27 \
3^{x} textgreater 3^3 \
x textgreater 3](https://tex.z-dn.net/?f=3%5E%7Bx%7D-3%5E%7Bx-3%7D+textgreater++26+%5C+%0A3%5E%7Bx%7D-+frac%7B3%5E%7Bx%7D%7D%7B3%5E3%7D+textgreater++26+%5C+%0A3%5E%7Bx%7D%281-+frac%7B1%7D%7B27%7D+%29+textgreater++26+%5C+%0A3%5E%7Bx%7D%2A+frac%7B26%7D%7B27%7D+textgreater++26+%5C+%0A3%5E%7Bx%7D+textgreater++26%2A+frac%7B27%7D%7B26%7D+%5C+%0A3%5E%7Bx%7D+textgreater++27+%5C+%0A3%5E%7Bx%7D+textgreater++3%5E3+%5C+%0Ax+textgreater++3+++ "3^{x}-3^{x-3} textgreater 26 \
3^{x}- frac{3^{x}}{3^3} textgreater 26 \
3^{x}(1- frac{1}{27} ) textgreater 26 \
3^{x}* frac{26}{27} textgreater 26 \
3^{x} textgreater 26* frac{27}{26} \
3^{x} textgreater 27 \
3^{x} textgreater 3^3 \
x textgreater 3")
x∈(3; +∞)
Ответ: (3; +∞)
x∈(5; +∞)
Ответ: (5; +∞)
б)
+ - +
--------- -1 --------- 3 ------------
\\\\\
x∈(-1; 3)
Ответ: (-1; 3)
в)
x∈(3; +∞)
Ответ: (3; +∞)
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