Let a and b be the vectors of the same magnitude such that (| a + b |+| a - b |)/(| a + b |-| a - b |)=√ 2 +1. Then (| a + b |^2)/(| a |^2) is:

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