Into which a) two parts, b) n parts should a given number be divided so that th

Into which a) two parts, b) n parts should a given number be divided so that the product of the parts is the greatest?

Prove that the sum of a) two, b) several numbers with a fixed product becomes smallest when the numbers are equal.

Let x₁ < x₂ < ... < xₙ. Find such a point x on the number line that the sum of the distances from x to xᵢ is minimised.

(Geometry problem) Find the minimum value of the expression: square root of (y - 2)² + 1 + square root of (x² + y²) + square root of (x - 2)² +