Подбором находим корни -4, 1.
(8·(x²-4))/((4x-8)²)=(8·(x²-4))/(16·(x-2)²)=(8·(x-2)·(x+2))/(2·8·<span>(x-2)²)=(x+2)/(2</span>·(x-2))
39.
1)
д=16-4×4×1=0
х=-4/2=-2
2)
д=144-4×4×9=0
х=12/2×4=3/2=1 1/2=1.5
38.
2)=-(1/9а^2-1/3аб+1/4б^2)=
=-(1/3а-1/2б)^2
![\displaystyle 1)..9*81^{1-2x}=27^{2-x} \\ \\ 3^{2}* \frac{3^{4}}{3^{8x}}= \frac{3^{6}}{3^{3x}} \\ \\ \frac{3^{6}}{3^{8x}}= \frac{3^{6}}{3^{3x}} \\ \\3^{8x}=3^{3x} \\ 8x=3x \\ x=0](https://tex.z-dn.net/?f=%5Cdisplaystyle+1%29..9%2A81%5E%7B1-2x%7D%3D27%5E%7B2-x%7D+%5C%5C++%5C%5C+3%5E%7B2%7D%2A+%5Cfrac%7B3%5E%7B4%7D%7D%7B3%5E%7B8x%7D%7D%3D+%5Cfrac%7B3%5E%7B6%7D%7D%7B3%5E%7B3x%7D%7D++%5C%5C++%5C%5C++%5Cfrac%7B3%5E%7B6%7D%7D%7B3%5E%7B8x%7D%7D%3D+%5Cfrac%7B3%5E%7B6%7D%7D%7B3%5E%7B3x%7D%7D+%5C%5C++%5C%5C3%5E%7B8x%7D%3D3%5E%7B3x%7D+%5C%5C+8x%3D3x+%5C%5C+x%3D0++++++++)
Ответ: {0}
![\displaystyle 2)..2^{x-4}-2^{x}=120](https://tex.z-dn.net/?f=%5Cdisplaystyle+2%29..2%5E%7Bx-4%7D-2%5E%7Bx%7D%3D120)
так как уменьшаемое меньше вычитаемого при любом х, то данная разность не может быть положительным числом.
Ответ: ∅
![\displaystyle 3)..10*5^{x-1}+5^{x+1}=7 \\ \\ \frac{10*5^{x}}{5}+5*5^{x}=7 \\ \\ 10*5^{x}+25*5^{x}=35 \\ 35*5^{x}=35 \\ 5^{x}=1 \\ x=0](https://tex.z-dn.net/?f=%5Cdisplaystyle+3%29..10%2A5%5E%7Bx-1%7D%2B5%5E%7Bx%2B1%7D%3D7+%5C%5C++%5C%5C++%5Cfrac%7B10%2A5%5E%7Bx%7D%7D%7B5%7D%2B5%2A5%5E%7Bx%7D%3D7+%5C%5C++%5C%5C+10%2A5%5E%7Bx%7D%2B25%2A5%5E%7Bx%7D%3D35+%5C%5C+35%2A5%5E%7Bx%7D%3D35+%5C%5C+5%5E%7Bx%7D%3D1+%5C%5C+x%3D0+++)
Ответ: {0}