Question

Решите уровнение под номером 9.
По фото

Answer 1

$displaystyle tt frac{1}{(x-2)^2}-frac{1}{x-2}-6=0::::: | : xne2\\ displaystyle tt frac{1-(x-2)-6(x-2)^2}{(x-2)^2}=0\\ displaystyle tt 1-x+2-6(x^2-4x+4)=0\displaystyle tt 3-x-6x^2+24x-24=0\displaystyle tt -6x^2+23x-21=0:::::|cdot (-1)\displaystyle tt 6x^2-23x+21=0\displaystyle tt D=(-23)^2-4cdot6cdot21=529-504=25\displaystyle tt sqrt{D}=sqrt{25}=5$

$displaystyle tt bold{x_1}=frac{23+5}{2cdot6}=frac{28}{12}=frac{7}{3}=bold{2frac{1}{3}}\\ displaystyle tt bold{x_2}=frac{23-5}{2cdot6}=frac{18}{12}=frac{3}{2}=bold{1,5}$

Answer 2

$dfrac{1}{(x-2)^2}-dfrac{1}{x-2}-6=0\ t=dfrac{1}{x-2}\ t^2-t-6=0\ t_1+t_2=1,t_1t_2=-6=>t=3;;;;;;t=-2\ dfrac{1}{x-2}=3=>x-2=dfrac{1}{3}=>x=2dfrac{1}{3}\ dfrac{1}{x-2}=-2=>x-2=-dfrac{1}{2}=>x=1dfrac{1}{2}\ OTBET: 2dfrac{1}{3},1dfrac{1}{2}$