Let (x₁, y₁), (x₂, y₂), …, (xₙ, yₙ) be n pairs of positive numbers. The arithmetic mean and geometric mean of any set of positive numbers (c₁, c₂, …, cₙ) are denoted by M(cᵢ), G(cᵢ) respectively.
Consider the following :
1M(xᵢ+yᵢ) = M(xᵢ) + M(yᵢ)
2G(xᵢyᵢ) = G(xᵢ)G(yᵢ)
Which of the above is/are correct ?

Question

Let (x₁, y₁), (x₂, y₂), …, (xₙ, yₙ) be n pairs of positive numbers. The arithmetic mean and geometric mean of any set of positive numbers (c₁, c₂, …, cₙ) are denoted by M(cᵢ), G(cᵢ) respectively.

Consider the following :

1M(xᵢ+yᵢ) = M(xᵢ) + M(yᵢ)
2G(xᵢyᵢ) = G(xᵢ)G(yᵢ)

Which of the above is/are correct ?

Accepted Answer

Option C: Both 1 and 2