Question

дайте пожалуйста развернутый ответ

Answer 1

$\displaystyle\bf\\\left \{ {{4x - 18 < 0} \atop {2 {x}^{2} - 5x + 3 \geqslant 0}} \right. \\ \\ 1) \: 4x - 18 < 0 \\ x - 4.5 < 0 \\ x < 4.5 \\ \\ 2) \: 2 {x}^{2} - 5x + 3 \geqslant 0 \\ 2 {x}^{2} - 5x + 3 = 0 \\ a = 2\\ b = - 5\\ c = 3 \\ D = {b}^{2} - 4ac = ( - 5) {}^{2} - 4 \times 2 \times 3 = 25 - 2 = 1 \\ x_{1} = \frac{5 - 1}{2 \times 2} = \frac{4}{4} = 1\\ x_{2} = \frac{5 + 1}{2 \times 2} = \frac{6}{4} = 1.5 \\ \\ {ax}^{2} + bx + c = a(x - x_{1})(x - x_{2}) \\ 2 {x}^{2} - 5x + 3 = 2(x - 1)(x - 1.5) \\ \\ (x - 1)(x - 1.5) \geqslant 0 \\ + + + [1] - - - [1.5] + + + \\ x \leqslant 1 \: \: \: and \: \: \: x \geqslant 1.5 \\ \\ 3) \\ \displaystyle\bf\\\left \{ {{x < 4.5} \atop {x \leqslant 1 \: \: \: and \: \: \: x \geqslant 1.5 }} \right. \\ \\ otvet \: \: \: x \: \epsilon \: ( - \propto; \: 1]U[1.5; \: 4.5)$