Let $\vec a$ and $\vec b$ be vectors of the same magnitude such that $\displaystyle \frac{\lvert\vec a+\vec b\rvert+\lvert\vec a-\vec b\rvert}{\lvert\vec a+\vec b\rvert-\lvert\vec a-\vec b\rvert}=\sqrt2+1.$ Then $\displaystyle \frac{\lvert\vec a+\vec b\rvert^{2}}{\lvert\vec a\rvert^{2}}$ is: