Question

Решите уравнение!
9 класс!

Answer 1

$\displaystyle \frac{x^2+2x+7}{x^2+2x+3}=4+2x+x^2$

$\displaystyle \frac{x^2+2x+3+4}{x^2+2x+3}=4+2x+x^2$

$\displaystyle 1+ \frac{4}{x^2+2x+3}=4+2x+x^2$

$\displaystyle \frac{4}{x^2+2x+3}=x^2+2x+3$

$x^2+2x+3=t$

$\displaystyle \frac{4}{t}=t 4=t^2 t=2; t=-2$

$\displaystyle \left \{ {{x^2+2x+3=2} \atop {x^2+2x+3=-2}} \right.$

$\displaystyle \left \{ {{x^2+2x+1=0} \atop {x^2+2x+5=0}} \right.$

$\displaystyle \left \{ {{(x+1)^2=0} \atop {x^2+2x+5=0}} \right.$

$\displaystyle \left \{ {{x=-1} \atop {x^2+2x+5 \neq 0}} \right.$

ответ : х=-1