Ответы
Ответ дал:
4
1) ![\frac{2x^{2}-2x+1}{2x-1} \leq 1 \frac{2x^{2}-2x+1}{2x-1} \leq 1](https://tex.z-dn.net/?f=+%5Cfrac%7B2x%5E%7B2%7D-2x%2B1%7D%7B2x-1%7D+%5Cleq+1+)
![\frac{2x^{2}-2x+1}{2x-1}- \frac{2x-1}{2x-1} \leq 0 \frac{2x^{2}-2x+1}{2x-1}- \frac{2x-1}{2x-1} \leq 0](https://tex.z-dn.net/?f=+%5Cfrac%7B2x%5E%7B2%7D-2x%2B1%7D%7B2x-1%7D-+%5Cfrac%7B2x-1%7D%7B2x-1%7D+%5Cleq+0)
![\frac{2x^{2}-2x+1-2x+1}{2x-1} \leq 0 \frac{2x^{2}-2x+1-2x+1}{2x-1} \leq 0](https://tex.z-dn.net/?f=+%5Cfrac%7B2x%5E%7B2%7D-2x%2B1-2x%2B1%7D%7B2x-1%7D+%5Cleq+0)
![\frac{2*(x^{2}-2x+1)}{2x-1} \leq 0 \frac{2*(x^{2}-2x+1)}{2x-1} \leq 0](https://tex.z-dn.net/?f=+%5Cfrac%7B2%2A%28x%5E%7B2%7D-2x%2B1%29%7D%7B2x-1%7D+%5Cleq+0)
![\frac{2*(x-1)^{2}}{2x-1} \leq 0 \frac{2*(x-1)^{2}}{2x-1} \leq 0](https://tex.z-dn.net/?f=+%5Cfrac%7B2%2A%28x-1%29%5E%7B2%7D%7D%7B2x-1%7D+%5Cleq+0)
1.1)![x-1=0 x-1=0](https://tex.z-dn.net/?f=x-1%3D0)
![x=1 x=1](https://tex.z-dn.net/?f=x%3D1)
1.2)![2x-1\ \textless \ 0 2x-1\ \textless \ 0](https://tex.z-dn.net/?f=2x-1%5C+%5Ctextless+%5C+0)
![x\ \textless \ \frac{1}{2} x\ \textless \ \frac{1}{2}](https://tex.z-dn.net/?f=x%5C+%5Ctextless+%5C++%5Cfrac%7B1%7D%7B2%7D)
Ответ: x∈(-бесконечность; 0.5)U{1}
2)![25x^2-3*|3-5x|\ \textless \ 30x-9 25x^2-3*|3-5x|\ \textless \ 30x-9](https://tex.z-dn.net/?f=25x%5E2-3%2A%7C3-5x%7C%5C+%5Ctextless+%5C+30x-9)
2.1)![\left \{ {{3-5x \geq 0} \atop {25x^2-3*(3-5x)\ \textless \ 30x-9}} \right. \left \{ {{3-5x \geq 0} \atop {25x^2-3*(3-5x)\ \textless \ 30x-9}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B3-5x+%5Cgeq+0%7D+%5Catop+%7B25x%5E2-3%2A%283-5x%29%5C+%5Ctextless+%5C+30x-9%7D%7D+%5Cright.+)
![\left \{ {x \leq 0.6} \atop {25x^2-9+15x-30x+9\ \textless \ 0}} \right. \left \{ {x \leq 0.6} \atop {25x^2-9+15x-30x+9\ \textless \ 0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7Bx+%5Cleq+0.6%7D+%5Catop+%7B25x%5E2-9%2B15x-30x%2B9%5C+%5Ctextless+%5C+0%7D%7D+%5Cright.+)
![\left \{ {x \leq 0.6} \atop {25x^2-15x\ \textless \ 0}} \right. \left \{ {x \leq 0.6} \atop {25x^2-15x\ \textless \ 0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7Bx+%5Cleq+0.6%7D+%5Catop+%7B25x%5E2-15x%5C+%5Ctextless+%5C+0%7D%7D+%5Cright.+)
![\left \{ {x \leq 0.6} \atop {x*(5x-3)\ \textless \ 0}} \right. \left \{ {x \leq 0.6} \atop {x*(5x-3)\ \textless \ 0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7Bx+%5Cleq+0.6%7D+%5Catop+%7Bx%2A%285x-3%29%5C+%5Ctextless+%5C+0%7D%7D+%5Cright.+)
![\left \{ {x \leq 0.6} \atop {0\ \textless \ x\ \textless \ 0.6}} \right. \left \{ {x \leq 0.6} \atop {0\ \textless \ x\ \textless \ 0.6}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7Bx+%5Cleq+0.6%7D+%5Catop+%7B0%5C+%5Ctextless+%5C+x%5C+%5Ctextless+%5C+0.6%7D%7D+%5Cright.+)
Решение: 0<x<0.6
2.2)![\left \{ {{3-5x\ \textless \ 0} \atop {25x^2-3*(-3+5x)\ \textless \ 30x-9}} \right. \left \{ {{3-5x\ \textless \ 0} \atop {25x^2-3*(-3+5x)\ \textless \ 30x-9}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7B3-5x%5C+%5Ctextless+%5C+0%7D+%5Catop+%7B25x%5E2-3%2A%28-3%2B5x%29%5C+%5Ctextless+%5C+30x-9%7D%7D+%5Cright.)
![\left \{ {{x\ \textgreater \ 0.6} \atop {25x^2+9-15x-30x+9\ \textless \ 0}} \right. \left \{ {{x\ \textgreater \ 0.6} \atop {25x^2+9-15x-30x+9\ \textless \ 0}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+0.6%7D+%5Catop+%7B25x%5E2%2B9-15x-30x%2B9%5C+%5Ctextless+%5C+0%7D%7D+%5Cright.)
![\left \{ {{x\ \textgreater \ 0.6} \atop {25x^2-45x+18\ \textless \ 0}} \right. \left \{ {{x\ \textgreater \ 0.6} \atop {25x^2-45x+18\ \textless \ 0}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+0.6%7D+%5Catop+%7B25x%5E2-45x%2B18%5C+%5Ctextless+%5C+0%7D%7D+%5Cright.)
![25x^2-45x+18=0, D=45^{2}-4*25*18=225=15^{2} 25x^2-45x+18=0, D=45^{2}-4*25*18=225=15^{2}](https://tex.z-dn.net/?f=25x%5E2-45x%2B18%3D0%2C+D%3D45%5E%7B2%7D-4%2A25%2A18%3D225%3D15%5E%7B2%7D)
![x_{1}= \frac{45-15}{50}=\frac{30}{50}=0.6 x_{1}= \frac{45-15}{50}=\frac{30}{50}=0.6](https://tex.z-dn.net/?f=x_%7B1%7D%3D+%5Cfrac%7B45-15%7D%7B50%7D%3D%5Cfrac%7B30%7D%7B50%7D%3D0.6)
![x_{2}= \frac{45+15}{50}=\frac{60}{50}=1.2 x_{2}= \frac{45+15}{50}=\frac{60}{50}=1.2](https://tex.z-dn.net/?f=x_%7B2%7D%3D+%5Cfrac%7B45%2B15%7D%7B50%7D%3D%5Cfrac%7B60%7D%7B50%7D%3D1.2)
![\left \{ {{x\ \textgreater \ 0.6} \atop {0.6\ \textless \ x\ \textless \ 1.2}} \right. \left \{ {{x\ \textgreater \ 0.6} \atop {0.6\ \textless \ x\ \textless \ 1.2}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+0.6%7D+%5Catop+%7B0.6%5C+%5Ctextless+%5C+x%5C+%5Ctextless+%5C+1.2%7D%7D+%5Cright.)
Решение: 0.6<x<1.2
Общее решение: x∈(0; 0.6)U(0.6; 1.2)
1.1)
1.2)
Ответ: x∈(-бесконечность; 0.5)U{1}
2)
2.1)
Решение: 0<x<0.6
2.2)
Решение: 0.6<x<1.2
Общее решение: x∈(0; 0.6)U(0.6; 1.2)
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