Question

Решите неравенствоа)б)

Answer 1

$\frac{x^{2}-x+2}{x^{2} -7x+6} <0, \\ x^{2}-x+2=0, \\ D=-7<0, a=1>0, \\x^{2}-x+2>0, \forall x\in R, \\ x^{2} -7x+6=0, \\x_1=1, x_2=6, \\ x^{2} -7x+6=(x-1)(x-6), \\ x^{2} -7x+6<0, \\(x-1)(x-6)<0, \\ 1<x<6.$

$\frac{4x^{2}+5x+3}{5- x^{2}}<0, \\ 4x^2+5x+3=0, \\ D=-23<0, a=4>0, \\ 4x^2+5x+3>0, \forall x\n R, \\ 5-x^2=0, \\ x^2=5, \\ x_1=- \sqrt{5}, x_2= \sqrt{5}, \\ 5-x^2=-(x+\sqrt{5})(x-\sqrt{5}), \\ 5-x^2<0, \\ -(x+\sqrt{5})(x-\sqrt{5})<0, \\ (x+\sqrt{5})(x-\sqrt{5})>0, \\ \left [ {{x<-\sqrt{5},} \atop {x>\sqrt{5}.}} \right.$