calculus - Limits problem to find the values of constants - a and b If $lim_{x to infty}(1+frac{a}{x}+frac{b}{x^2})^{2x}=e^2$ Find the value of $a$ and $b$.

Problem :

If $\lim\limits_{x \to \infty}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2x}=e^2$ Find the value of $a$ and $b$.

Please suggest how to proceed this problem :

If we know that $\lim\limits_{x \to \infty}\left( 1+\frac{1}{x}\right)^x= e$

Will this work somehow... please suggest