Все решение представлено на фото
ОДЗ : x > 0
![log_{4}^{2}x+log_{4}\sqrt{x}>1,5\\\\log_{4}^{2}x+\frac{1}{2}log_{4}x-\frac{3}{2}>0\\\\2log_{4}^{2}x+log_{4}x-3>0\\\\log_{4}x=m\\\\2m^{2}+m-3>0\\\\2m^{2}+m-3=0\\\\D=1^{2}-4*2*(-3)=1+24=25=5^{2}\\\\m_{1}=\frac{-1+5}{4}=1\\\\m_{2}=\frac{-1-5}{4}=-\frac{3}{2} \\\\2(m-1)(m+\frac{3}{2})>0\\\\(m-1)(m+1,5)>0](https://tex.z-dn.net/?f=log_%7B4%7D%5E%7B2%7Dx%2Blog_%7B4%7D%5Csqrt%7Bx%7D%3E1%2C5%5C%5C%5C%5Clog_%7B4%7D%5E%7B2%7Dx%2B%5Cfrac%7B1%7D%7B2%7Dlog_%7B4%7Dx-%5Cfrac%7B3%7D%7B2%7D%3E0%5C%5C%5C%5C2log_%7B4%7D%5E%7B2%7Dx%2Blog_%7B4%7Dx-3%3E0%5C%5C%5C%5Clog_%7B4%7Dx%3Dm%5C%5C%5C%5C2m%5E%7B2%7D%2Bm-3%3E0%5C%5C%5C%5C2m%5E%7B2%7D%2Bm-3%3D0%5C%5C%5C%5CD%3D1%5E%7B2%7D-4%2A2%2A%28-3%29%3D1%2B24%3D25%3D5%5E%7B2%7D%5C%5C%5C%5Cm_%7B1%7D%3D%5Cfrac%7B-1%2B5%7D%7B4%7D%3D1%5C%5C%5C%5Cm_%7B2%7D%3D%5Cfrac%7B-1-5%7D%7B4%7D%3D-%5Cfrac%7B3%7D%7B2%7D+%5C%5C%5C%5C2%28m-1%29%28m%2B%5Cfrac%7B3%7D%7B2%7D%29%3E0%5C%5C%5C%5C%28m-1%29%28m%2B1%2C5%29%3E0)
+ - +
__________₀____________₀__________m
- 1,5 1
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![1)log_{4} x<-\frac{3}{2}\\\\x<4^{-\frac{3}{2} } \\\\x<(\frac{1}{4})^{\frac{3}{2} }\\\\x<\sqrt{(\frac{1}{4})^{3}}\\\\x<\frac{1}{8}\\\\2)log_{4}x>1\\\\x>4](https://tex.z-dn.net/?f=1%29log_%7B4%7D+x%3C-%5Cfrac%7B3%7D%7B2%7D%5C%5C%5C%5Cx%3C4%5E%7B-%5Cfrac%7B3%7D%7B2%7D+%7D+%5C%5C%5C%5Cx%3C%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B%5Cfrac%7B3%7D%7B2%7D+%7D%5C%5C%5C%5Cx%3C%5Csqrt%7B%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B3%7D%7D%5C%5C%5C%5Cx%3C%5Cfrac%7B1%7D%7B8%7D%5C%5C%5C%5C2%29log_%7B4%7Dx%3E1%5C%5C%5C%5Cx%3E4)
Ответ : x ∈ (0 ; 1/8) ∪ (4 ; + ∞)
A) f(x)=2x²-x
2x²-x=0
2x(x-0,5)=0
x1=0
x2=0,5
g) 2x-5x²=0
-5x(x-0,4)=0
x1=0
<span>x2=0,4</span>
Держи)
Надеюсь разберёшься в моём почерке))
Формула, которой нужно пользоваться, обведена в рамочку.
По ней делается всё задание.
![\boxed{a^{-n} = \dfrac{1}{a^n} } \\ \\ \dfrac{1}{24^7} = 24^{-7} \\ \\ \dfrac{1}{9} = 9^{-1} \\ \\ \dfrac{1}{a^4} = a^{-4} } \\ \\ \dfrac{1}{(3b)^5} = (3b)^{-5} \\ \\ \dfrac{1}{c} = c^{-1}](https://tex.z-dn.net/?f=%5Cboxed%7Ba%5E%7B-n%7D%20%3D%20%5Cdfrac%7B1%7D%7Ba%5En%7D%20%7D%20%5C%5C%20%5C%5C%20%5Cdfrac%7B1%7D%7B24%5E7%7D%20%3D%2024%5E%7B-7%7D%20%5C%5C%20%5C%5C%20%5Cdfrac%7B1%7D%7B9%7D%20%3D%209%5E%7B-1%7D%20%5C%5C%20%5C%5C%20%5Cdfrac%7B1%7D%7Ba%5E4%7D%20%3D%20a%5E%7B-4%7D%20%7D%20%5C%5C%20%5C%5C%20%5Cdfrac%7B1%7D%7B%283b%29%5E5%7D%20%3D%20%283b%29%5E%7B-5%7D%20%5C%5C%20%5C%5C%20%5Cdfrac%7B1%7D%7Bc%7D%20%3D%20c%5E%7B-1%7D%20)