$6.257 x^{3}-(2 a+1) x^{2}+\left(a^{2}+2 a-b^{2}\right) x+\left(b^{2}-a^{2}\right)=0$.

Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly.

$6.257 x^{3}-(2 a+1) x^{2}+\left(a^{2}+2 a-b^{2}\right) x+\left(b^{2}-a^{2}\right)=0$.
Solution. The given equation is a particular case of the model equation (1) if we set $v=1, u=a, w=b$.

Answer: $x_{1}=1, x_{2,3}=a \pm b$.