If m is the A.M. of two distinct real numbers l and n(l, n > 1) a

Question:

If $\mathrm{m}$ is the A.M. of two distinct real numbers $l$ and $n(1, n>1)$ and $G_{1}, G_{2}$ and $G_{3}$ are three geometric means between 1 and $n$, then $G_{1}^{4}+2 G_{2}^{4}+G_{3}^{4}$ equals -

  1. $4 \operatorname{lmn}^{2}$

  2. $41^{2} m^{2} n^{2}$

  3. $4 l^{2} \mathrm{mn}$

  4. $4 \operatorname{lm}^{2} n$


Correct Option: , 4

Solution:

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