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min, max of x^2 + 2y^2 + 3z^2 when x^2 + y^2 + z^2 = 1

Source: 1968 Swedish Mathematical Competition p1

March 21, 2021
algebraminmaxinequalities

Problem Statement

Find the maximum and minimum values of x2+2y2+3z2x^2 + 2y^2 + 3z^2 for real x,y,zx, y, z satisfying x2+y2+z2=1x^2 + y^2 + z^2 = 1.
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