Tex]f(x)=x^3\\ F(x)= \frac{x^4}{4} [/tex]
![\sqrt{36^{x} -3*6^{x+1}+81}+6^{x}\leq 9-\sqrt{16^{x}-9*4^{x}+18}\\\\\sqrt{(6^{x})^{2}-3*6^{x}*6+81}+6^{x}\leq9- \sqrt{(4^{x})^{2}-9*4^{x}+18}\\\\\sqrt{(6^{x}-9)^{2}}+6^{x}\leq9-\sqrt{(4^{x}-3)(4^{x}-6)}](https://tex.z-dn.net/?f=%5Csqrt%7B36%5E%7Bx%7D%20-3%2A6%5E%7Bx%2B1%7D%2B81%7D%2B6%5E%7Bx%7D%5Cleq%209-%5Csqrt%7B16%5E%7Bx%7D-9%2A4%5E%7Bx%7D%2B18%7D%5C%5C%5C%5C%5Csqrt%7B%286%5E%7Bx%7D%29%5E%7B2%7D-3%2A6%5E%7Bx%7D%2A6%2B81%7D%2B6%5E%7Bx%7D%5Cleq9-%20%5Csqrt%7B%284%5E%7Bx%7D%29%5E%7B2%7D-9%2A4%5E%7Bx%7D%2B18%7D%5C%5C%5C%5C%5Csqrt%7B%286%5E%7Bx%7D-9%29%5E%7B2%7D%7D%2B6%5E%7Bx%7D%5Cleq9-%5Csqrt%7B%284%5E%7Bx%7D-3%29%284%5E%7Bx%7D-6%29%7D)
Найдём ОДЗ для корня стоящего справа :
![(4^{x}-3)(4^{x}-6)\geq 0\\\\\left[\begin{array}{ccc}4^{x}\leq 3 \\4^{x}\geq6 \end{array}\right \\\\\left[\begin{array}{ccc}x \leq log_{4}3\\x \geq log_{4}6 \end{array}\right\\\\x\in(-\infty;log_{4}3]\cup[log_{4}6;+\infty)](https://tex.z-dn.net/?f=%284%5E%7Bx%7D-3%29%284%5E%7Bx%7D-6%29%5Cgeq%200%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5E%7Bx%7D%5Cleq%203%20%5C%5C4%5E%7Bx%7D%5Cgeq6%20%20%5Cend%7Barray%7D%5Cright%20%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%20%5Cleq%20log_%7B4%7D3%5C%5Cx%20%5Cgeq%20log_%7B4%7D6%20%20%5Cend%7Barray%7D%5Cright%5C%5C%5C%5Cx%5Cin%28-%5Cinfty%3Blog_%7B4%7D3%5D%5Ccup%5Blog_%7B4%7D6%3B%2B%5Cinfty%29)
![\sqrt{(6^{x}-9)^{2}}+6^{x}\leq9-\sqrt{16^{x}-9*4^{x}+18}\\\\\sqrt{16^{x}-9*4^{x}+18}\leq9-6^{x} -|6^{x} -9|](https://tex.z-dn.net/?f=%5Csqrt%7B%286%5E%7Bx%7D-9%29%5E%7B2%7D%7D%2B6%5E%7Bx%7D%5Cleq9-%5Csqrt%7B16%5E%7Bx%7D-9%2A4%5E%7Bx%7D%2B18%7D%5C%5C%5C%5C%5Csqrt%7B16%5E%7Bx%7D-9%2A4%5E%7Bx%7D%2B18%7D%5Cleq9-6%5E%7Bx%7D%20-%7C6%5E%7Bx%7D%20-9%7C)
Раскроем модуль :
![1)6^{x}-9\leq 0\Rightarrow \sqrt{16^{x} -9*4^{x}+18} \leq 9-6^{x}+6^{x}-9\\\\\sqrt{16^{x} -9*4^{x}+18}\leq0](https://tex.z-dn.net/?f=1%296%5E%7Bx%7D-9%5Cleq%200%5CRightarrow%20%5Csqrt%7B16%5E%7Bx%7D%20-9%2A4%5E%7Bx%7D%2B18%7D%20%5Cleq%209-6%5E%7Bx%7D%2B6%5E%7Bx%7D-9%5C%5C%5C%5C%5Csqrt%7B16%5E%7Bx%7D%20-9%2A4%5E%7Bx%7D%2B18%7D%5Cleq0)
Корень квадратный не может принимать значения меньше нуля, значит: при ![x\leq log_{6}9](https://tex.z-dn.net/?f=x%5Cleq%20log_%7B6%7D9)
![\sqrt{16^{x}-9*4^{x}+18}=0\\\\16^{x}-9*4^{x}+18=0\\\\x_{1}=log_{4}3\\\\x_{2} =log_{4}6](https://tex.z-dn.net/?f=%5Csqrt%7B16%5E%7Bx%7D-9%2A4%5E%7Bx%7D%2B18%7D%3D0%5C%5C%5C%5C16%5E%7Bx%7D-9%2A4%5E%7Bx%7D%2B18%3D0%5C%5C%5C%5Cx_%7B1%7D%3Dlog_%7B4%7D3%5C%5C%5C%5Cx_%7B2%7D%20%3Dlog_%7B4%7D6)
Сравним
![Log_{4}6ilog_{6}9\\\\log_{4}6-1=log_{4}6-log_{4}4=log_{4}\frac{6}{4}=log_{4}\frac{3}{2}\\\\log_{6}9-1=log_{6}9-log_{6}6=log_{6}\frac{9}{6}=log_{6}\frac{3}{2}\\\\4<6 \Rightarrow log_{4} \frac{3}{2}> log_{6}\frac{3}{2}](https://tex.z-dn.net/?f=Log_%7B4%7D6ilog_%7B6%7D9%5C%5C%5C%5Clog_%7B4%7D6-1%3Dlog_%7B4%7D6-log_%7B4%7D4%3Dlog_%7B4%7D%5Cfrac%7B6%7D%7B4%7D%3Dlog_%7B4%7D%5Cfrac%7B3%7D%7B2%7D%5C%5C%5C%5Clog_%7B6%7D9-1%3Dlog_%7B6%7D9-log_%7B6%7D6%3Dlog_%7B6%7D%5Cfrac%7B9%7D%7B6%7D%3Dlog_%7B6%7D%5Cfrac%7B3%7D%7B2%7D%5C%5C%5C%5C4%3C6%20%5CRightarrow%20log_%7B4%7D%20%5Cfrac%7B3%7D%7B2%7D%3E%20log_%7B6%7D%5Cfrac%7B3%7D%7B2%7D)
Значит подходит только корень x₁ .
![2)6^{x}-9>0\\\\\sqrt{16^{x}-9*4^{x}+18}\leq9-6^{x}-6^{x}+9\\\\9-6^{x}-6^{x}+9=18-2*6^{x}<0,tak .kak 6^{x}>9](https://tex.z-dn.net/?f=2%296%5E%7Bx%7D-9%3E0%5C%5C%5C%5C%5Csqrt%7B16%5E%7Bx%7D-9%2A4%5E%7Bx%7D%2B18%7D%5Cleq9-6%5E%7Bx%7D-6%5E%7Bx%7D%2B9%5C%5C%5C%5C9-6%5E%7Bx%7D-6%5E%7Bx%7D%2B9%3D18-2%2A6%5E%7Bx%7D%3C0%2Ctak%20.kak%206%5E%7Bx%7D%3E9)
решений нет
![Otvet:\boxed{ log_{4}3}](https://tex.z-dn.net/?f=Otvet%3A%5Cboxed%7B%20log_%7B4%7D3%7D)
1. 2а-а и -4х+10х= а+6x
2. (раскрываем скобки) 2в+3в-5-в-1= 2в+3в-в и -5-1= 4в-6
3. (перемножаем) 3а-12в+12в+2а= 3а+2а и -12в+12в(зачеркиваем так как числа с разными знакими)= 5а