If ' m ' is the arithmetic mean of two distinct real numbers l and n(l, n>1) and G_1, G_2 and G_3 are three geometric means between l and n, then…

If ' $\displaystyle m$ ' is the arithmetic mean of two distinct real numbers $\displaystyle l$ and $\displaystyle n(l, n>1)$ and $\displaystyle \mathrm{G}_1, \mathrm{G}_2$ and $\displaystyle \mathrm{G}_3$ are three geometric means between $\displaystyle l$ and $\displaystyle n$, then $\displaystyle \mathrm{G}_1{ }^4+2 \mathrm{G}_2{ }^4+\mathrm{G}_3{ }^4$ equals