Question

$sqrt{x-6}* sqrt{x-12} textless x-1$

Answer 1

$sqrt{x-6}cdot sqrt{x-12} textless x-1$

$left{begin{matrix} x-1 & textgreater &0 \ (x-6)(x-12) & textless &(x-1)^2 \ x-6 &geqslant &0 \ x-12 &geqslant &0 end{matrix}right.$

$x-1 textgreater 0\ x textgreater 1\ xin(1;+infty)$


$(x-6)(x-12) textless (x-1)^2\ (x-6)(x-12)-(x-1)^2 textless 0\ x^2-18x+72-x^2+2x-1 textless 0\ -16x textless -71\\ x textgreater frac{71}{16}\\ xin(frac{71}{16};+infty)$


$x-6geqslant 0\ xgeqslant 6\ xin[6;+infty)\\\ x-12geqslant 0\ xgeqslant 12\ xin(12;+infty)$

Ответ: $xin[12;+infty)$