Задача

[Гост]

IMG_20240428_152934_425.jpg (38.21 KiB) Прегледано 182 пъти

[ammornil]

[tex]4\frac{4}{10}x+\left(\frac{1}{2}-x\right)\left(\frac{1}{2}+x\right)-3\ge{}x(2-x)+\frac{5}{2}\left(x-\frac{7}{5}\right), \quad \text{ДМ: } \forall{x}\in\mathbb{R}\\ \quad \\ \frac{22}{5}x+\left(\frac{1}{2}\right)^{2}\cancel{-x^{2}}-3\ge{}2x\cancel{-x^{2}}+\frac{5}{2}x-\frac{7}{2} \quad \Leftrightarrow \quad \underbrace{\frac{22x}{5}+\frac{1}{4}-3-2x-\frac{5x}{2}+\frac{7}{2}\ge{0}}_{20} \Leftrightarrow \\ \Leftrightarrow \quad 4\cdot{22x}+5\cdot{1}-20\cdot{3}-20\cdot{2x}-10\cdot{5x}+10\cdot{7}\ge{0} \quad \Leftrightarrow \\ \Leftrightarrow \quad 88x+5-60-40x-50x+70 \ge{0} \quad \Leftrightarrow \\ \Leftrightarrow \quad -2x\ge{}-15 \quad \Leftrightarrow \\ \Leftrightarrow \quad x \le{}\frac{15}{2} \\ \begin{cases} x\le{}7\frac{1}{2} \\ x\in\mathbb{N} \end{cases} \Rightarrow x \in \{1, 2, 3, 4, 5, 6, 7\} \Rightarrow \sum_{x=1}^{7}{x}=28[/tex]