A Three-Variable Radical Max

8/10SubstitutionalgebraAM-GMinequality

Problem

Positive reals x,y,zx, y, z satisfy

x2+y2+z=1.\sqrt{x^2 + y^2} + z = 1.

Find the maximum value of xy+2xzxy + 2xz.

Answer

Solution

Difficulty8/10
TopicsSubstitution, algebra, AM-GM, inequality

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