Question

Распишите пожалуйста подробно решение! 30Баллов!!

Answer 1

$1)\; \; x^3-3x^2-8x+24=0\\\\x^2(x-3)-8(x-3)=0\\\\(x-3)(x^2-8)=0\\\\(x-3)(x-\sqrt8)(x+\sqrt8)=0\\\\(x-3)(x-2\sqrt2)(x+2\sqrt2)=0\\\\x_1=3\; ,\; \; x_2=2\sqrt2\; ,\; x_3=-2\sqrt2\\\\2)\; \; \left \{ {{4(9x+3)-9(4x+3)>3x\; ,} \atop {(x-2)(x+9)<0\; .}} \right. \; \left \{ {{36x+12-36x-27>3x} \atop {x\in (-9,2)}} \right. \; \left \{ {{3x<-15} \atop {x\in (-9,2)}} \right. \\\\\left \{ {{x<-5} \atop {x\in (-9,2)}} \right. \; \left \{ {{x\in (-\infty ,-5)} \atop {x\in (-9,2)}} \right. \; \; \Rightarrow \; \; \; x\in (-9,-5)$

$\star \; \; (x-2)(x+9)<0\; \; \; \qquad +++(-9)---(2)+++\\\\x\in (-9,2)$