![3*4^x-5*6^x+2*9^x \leq 0 \\ \\ 3*4^x-5*6^x+2*9^x= 0 \ | :9^x, \ 9^x \neq 0 \\ \\ 3* (\frac{4}{9} )^x-5* (\frac{6}{9} )^x+2=0 \\ \\ 3* (\frac{2}{3} )^{2x}-5* (\frac{2}{3} )^x+2=0 \\ \\ (\frac{2}{3} )^x=t, \ t\ \textgreater \ 0 \\ \\ 3t^2-5t+2=0 \\ \\ D=25-24=1 \\ \\ t_1= \frac{5-1}{6}= \frac{2}{3} \\ \\ t_2= \frac{5+1}{6} =1 \\ \\ 1) (\frac{2}{3} )^x=\frac{2}{3} \\ \\ x=1 \\ \\ 2) \ (\frac{2}{3})^x=1 \\ \\ (\frac{2}{3})^x=(\frac{2}{3})^0 \\ \\ x=0](https://tex.z-dn.net/?f=3%2A4%5Ex-5%2A6%5Ex%2B2%2A9%5Ex+%5Cleq+0+%5C%5C++%5C%5C+3%2A4%5Ex-5%2A6%5Ex%2B2%2A9%5Ex%3D+0+%5C+%7C++%3A9%5Ex%2C+%5C+9%5Ex+%5Cneq+0+%5C%5C++%5C%5C+3%2A+%28%5Cfrac%7B4%7D%7B9%7D+%29%5Ex-5%2A+%28%5Cfrac%7B6%7D%7B9%7D+%29%5Ex%2B2%3D0+%5C%5C++%5C%5C+3%2A+%28%5Cfrac%7B2%7D%7B3%7D+%29%5E%7B2x%7D-5%2A+%28%5Cfrac%7B2%7D%7B3%7D+%29%5Ex%2B2%3D0+%5C%5C++%5C%5C+%28%5Cfrac%7B2%7D%7B3%7D+%29%5Ex%3Dt%2C+%5C+t%5C+%5Ctextgreater+%5C+0+%5C%5C++%5C%5C+3t%5E2-5t%2B2%3D0+%5C%5C++%5C%5C+D%3D25-24%3D1+%5C%5C++%5C%5C+t_1%3D+%5Cfrac%7B5-1%7D%7B6%7D%3D+%5Cfrac%7B2%7D%7B3%7D+++%5C%5C++%5C%5C+t_2%3D+%5Cfrac%7B5%2B1%7D%7B6%7D+%3D1+%5C%5C++%5C%5C+1%29+%28%5Cfrac%7B2%7D%7B3%7D+%29%5Ex%3D%5Cfrac%7B2%7D%7B3%7D+%5C%5C++%5C%5C+x%3D1+%5C%5C+%5C%5C+2%29+%5C+%28%5Cfrac%7B2%7D%7B3%7D%29%5Ex%3D1+%5C%5C++%5C%5C+%28%5Cfrac%7B2%7D%7B3%7D%29%5Ex%3D%28%5Cfrac%7B2%7D%7B3%7D%29%5E0+%5C%5C++%5C%5C+x%3D0)
![3*4^x-5*6^x+2*9^x \leq 0 \\ \\ +++++[0]----[1]+++++\ \textgreater \ x \\ \\ x \in [0;1]](https://tex.z-dn.net/?f=3%2A4%5Ex-5%2A6%5Ex%2B2%2A9%5Ex+%5Cleq+0+%5C%5C+%5C%5C+%2B%2B%2B%2B%2B%5B0%5D----%5B1%5D%2B%2B%2B%2B%2B%5C+%5Ctextgreater+%5C+x+%5C%5C++%5C%5C+x+%5Cin+%5B0%3B1%5D)
Целые решения: 0; 1
количество целых решений: 2
Ответ: 2
-1. Решение задания приложено. Не банально возводим в степень 2,5, не используем калькулятор, а используем свойства степеней и знание перехода десятисной дроби к обыкновенной.
= cos(2π+π/3)-sin(2π-π/6)= cos(π/3)+sin(π/6)= 1/2+1/2 = 1
1) 0,7×(-0,3)/0,7+(-0,3)=-0,21/0,4 = -0, 525
2) 33/37
5х+3у=20 умножаем на 2
2х-4у=21 умножаем на -5
10х+6у=40
-10х+20у= -105
(10х и-10х сокращаются)
остается:26у= -105
у= -65 разделить на 26
у= -2,5