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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 …

Q1

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. The \(G_1{ }^4+G_2{ }^4+G_3{ }^4+G_1{ }^2 G_3{ }^2\) is equal to

[JEE Main 2023, 15 Apr (Shift 1)]

a

\(2\left( A _1+A_2\right) G_1 G_2\)

b

\(\left( A _1+A_2\right)^2 G_1 G_3\)

c

\(\left( A _1+A_2\right) G_1^2 G_3^2\)

d

\(2\left( A _1+A_2\right) G_1{ }^2 G_3{ }^2\)

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