Question

Решить неравенство: (2/7)^(3×(x-1/3))<(4/49)^(x^2)

Answer 1

$( frac{2}{7} )^{3(x- frac{1}{3}) } textless ( frac{4}{49} )^{x^2}$
$( frac{2}{7} )^{3(x- frac{1}{3}) } textless ( frac{2}{7} )^{2x^2}$
${3(x- frac{1}{3}) } textgreater {2x^2}$
$3x-1 textgreater {2x^2}$
$3x-1 - 2x^2 textgreater 0$
$2x^2-3x+1 textless 0$
$D=(-3)^2-4*2*1=1$
$x_1= frac{3+1}{4}=1$
$x_2= frac{3-1}{4}=0.5$

---------+-------(0.5)-------- - -------(1)--------+----------
                            /////////////////////

Ответ: (0.5;1)