Question

Gente nao consigo fazer PFFF me ajudem

Answer 1

$x(x+1)=m(x+2)~~\Rightarrow~~x^2+x=mx+2m$

$x^2+x-mx-2m=0~~\Rightarrow\boxed{x^2+(1-m)x-2m=0}$

Se as raízes dessa equação são iguais, devemos ter $\Delta=0$.

Assim, $(1-m)^2-4\cdot1\cdot(-2m)=0$.

$1-2m+m^2+8m=0$

$m^2+6m+1=0$

$\Delta=6^2-4\cdot1\cdot1=36-4=32$.

$m=\dfrac{-6\pm4\sqrt{2}}{2}$

$\boxed{m'=-3+2\sqrt{2}}$

$\boxed{m"=-3-2\sqrt{2}}$