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        

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