Let $A_{1}$ and $A_{2}$ be two arithmetic means and $G_{1}, G_{2}, G_{3}$ be three geometric means of two distinct positive numbers. Then $G_{1}^{4}+G_{2}^{4}+G_{3}^{4}+G_{1}^{2} G_{3}^{2}$ is equal to :

Question

Let $A_{1}$ and $A_{2}$ be two arithmetic means and $G_{1}, G_{2}, G_{3}$ be three geometric

means of two distinct positive numbers. Then $G_{1}^{4}+G_{2}^{4}+G_{3}^{4}+G_{1}^{2} G_{3}^{2}$ is equal to :

$\left(A_{1}+A_{2}\right)^{2} G_{1} G_{3}$

$\left(A_{1}+A_{2}\right) G_{1}^{2} G_{3}^{2}$

$2\left(A_{1}+A_{2}\right) G_{1}^{2} G_{3}^{2}$

$2\left(A_{1}+A_{2}\right) G_{1} G_{3}$

Solution

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