Let H: x^2/(a^2)-y^2/(b^2)=1, a >0, b >0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4(2 √ 2 +√ 14 ). If…

Let $\displaystyle \mathrm{H}: \frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1, \mathrm{a}>0, \mathrm{~b}>0$, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $\displaystyle 4(2 \sqrt{2}+\sqrt{14})$. If the eccentricity H is $\displaystyle \frac{\sqrt{11}}{2}$, then the value of $\displaystyle \mathrm{a}^2+\mathrm{b}^2$ is equal to \_\_\_\_.