(200/x) -1=200/(x+10) Ако може някои да я реши

[Гост]

(200/x) -1=200/(x+10)

[Xixibg]

[tex]\frac{200}{x}-1=\frac{200}{x+10}[/tex]
[tex]\frac{200}{x}-\frac{1}{1}=\frac{200}{x+10}[/tex]
[tex]\frac{200(x+10)}{x(x+10)}-\frac{x(x+10)}{x(x+10)}=\frac{200x}{x(x+10)} ; x\ne 0 ; x\ne -10[/tex]
[tex]200(x+10)-x(x+10)=200x[/tex]
[tex]\cancel{200x}+2000-x^2-10x=\cancel{200x}[/tex]
[tex]-x^2-10x+2000=0 (*(-1))[/tex]
[tex]x^2+10x-2000=0[/tex]
[tex]D=100+8000=8100=90^2[/tex]
[tex]x_1=\frac{-10+90}{2}=40 ; x_2=\frac{-10-90}{2}=-50[/tex]