ГДЗ по алгебре 9 класс Макарычев ФГОС Задание 339

\[\boxed{\text{340.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ 2 \cdot (x + 1)(x - 3) >\]

\[> (x + 5)(x - 7)\]

\[2 \cdot \left( x^{2} + x - 3x - 3 \right) >\]

\[> x^{2} - 7x + 5x - 35\]

\[2x^{2} - 4x - 6 - x^{2} + 2x + 35 >\]

\[> 0\]

\[x^{2} - 2x + 29 > 0\]

\[x^{2} - 2x + 1 + 28 > 0\]

\[(x - 1)^{2} + 28 > 0\]

\[неравенство\ верно\ при\ любом\ \]

\[значении\ \text{x.}\]

\[\textbf{б)}\frac{1}{4} \cdot (x + 5)(x - 7) \leq\]

\[\leq (x + 2)(x - 4)\]

\[x^{2} + 5x - 7x - 35 \leq\]

\[\leq 4 \cdot \left( x^{2} - 4x + 2x - 8 \right)\]

\[x^{2} - 2x - 35 \leq 4x^{2} - 8x - 32\]

\[3x^{2} - 6x + 3 \geq 0\]

\[3 \cdot \left( x^{2} - 2x + 1 \right) \geq 0\]

\[3 \cdot (x - 1)^{2} \geq 0\]

\[неравенство\ верно\ при\ любом\ \]

\[значении\ \text{x.}\]