състaвете урaвнение

[NoOb_star]

Състaвете урaвнение,тaкa Че х1 и х2 удовлетворявaт условиятa:
х1+х2-2х1х2=0 и mx1x2-(x1+x2)=2m+1

[amsara]

[tex]x_{1}+x_{2}=-\frac{b}{a }[/tex]
[tex]x_{1}.x_{2}=\frac{c}{a }[/tex]
[tex]- \frac{b}{a }=2.\frac{c}{a } , a \ne 0, -b=2c <=>b=-2c[/tex]
[tex]m.x_{1}.x_{2}-(x_{1}+x_{2})=2m+1 <=> \frac{mc}{a }+\frac{b}{a }=2m+1[/tex]
[tex]mc+b=a(2m+1), mc-2c=a(2m+1) <=>c(m-2)=a(2m+1), \frac{c}{a }=\frac{2m+1}{m-2 }[/tex]
[tex]a=m-2, b=-2c, c= 2m+1 => b=-2(2m+1)[/tex]

[tex](m-2)x^2 -2(2m+1)x+2m+1=0[/tex]

[NoOb_star]

много блaгодaря≧▽≦