Question

Допоможіть будь ласка 25б

Answer 1

$\displaystyle\bf\\\frac{3x-x^{2} }{2} -\frac{2x+5}{3} \geq 4-3x\\\\\\\frac{3x-x^{2} }{2} \cdot 6-\frac{2x+5}{3} \cdot 6\geq (4-3x)\cdot 6\\\\\\(3x-x^{2} )\cdot 3-(2x+5)\cdot 2\geq 24-18x\\\\\\9x-3x^{2} -4x-10\geq 24-18x\\\\\\5x-3x^{2}-10-24+18x\geq 0\\\\\\-3x^{2} +23x-34\geq 0\\\\\\3x^{2} -23x+34\leq 0\\\\\\3x^{2} -23x+34=0\\\\D=(-23)^{2} -4\cdot 3\cdot 34=529-408=121=11^{2} \\\\\\x_{1} =\frac{23-11}{6} =2\\\\\\x_{2} =\frac{23+11}{6} =5\frac{2}{3}$

$\displaystyle\bf\\3x^{2} -23x+34=3\cdot\Big(x-2\Big)\cdot\Big(x-5\frac{2}{3} \Big)\\\\\\\Big(x-2\Big)\cdot\Big(x-5\frac{2}{3} \Big)\leq 0\\\\\\+ + + + + \Big[2\Big]- - - - - \Big[5\frac{2}{3} \Big]+ + + + + \\\\\\x\in\Big[2 \ ; \ 5\frac{2}{3} \Big]\\\\\\Otvet \ : \ 5$