If p, g₁, g₂ and q are in GP and m is the arithmetic mean of p and q, then g₁²/g₂ + g₂²/g₁ is equal to

Since p, g₁, g₂, q are in GP with common ratio r, we have g₁ = pr, g₂ = pr², q = pr³. Then g₁²/g₂ = p²r²/(pr²) = p, and g₂²/g₁ = p²r⁴/(pr) = pr³ = q. So g₁²/g₂ + g₂²/g₁ = p + q = 2m, since m = (p+q)/2.