Question

Решите неравенство x/6< =(x^2-1)/5

Answer 1

$\frac{x}{6} \leq \frac{ (x^{2} -1)}{5} |*30$
5X≤(x²-1)*6
5x≤6x²-6
-6x²+5x+6≤0 |*(-1)
6x²-5x-6≥0

x1,2 =  5 ± √25+144  =     5 ± 13
           __________         ______              ⇒x1 = 1,5; x2 = -2/3
                  12                    12        

$6(x+ \frac{2}{3})(x-1,5) \left \{ {{x+ \frac{2}{3} 0 } \atop {x-1,5 < 0}} \right. \left \{ {{x+ \frac{2}{3} < 0} \atop {x-1,5 0}} \right. \\ \left \{ {{x- \frac{2}{3} } \atop {x<1,5}} \right. \left \{ {{x<- \frac{2}{3} } \atop {x1,5}} \right. \\ x- \frac{2}{3} ; x<1,5 \\ - \frac{2}{3} < x < 1,5$
x принадлежит (-2/3;1,5)