Question

Sa se rezolve ecuatia:

$\frac{5}{x+m}- \frac{1}{m-x}=2+ \frac{10m}{m^2-x^2}$

Mersi.

Answer 1

$\frac{5m-5x-x-m}{ m^{2}- x^{2} }= \frac{2 m^{2}-2 x^{2} +10m }{ m^{2}- x^{2} } \\ 4m-6x=2 m^{2}-2x^2+10m \\ 2x^2-6x-2m^2-6m=0 \\ x^{2} -3x-m^2-3=0$
Δ=9+4(m^2+3)=4m^2+21
$x_{1} = \frac{3- \sqrt{4m^2+21} }{2} \\ x_{2}= \frac{3+ \sqrt{4m^2+21} }{2}$