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PrecalculusSuperchallengeSystems, Matrices, and Determinants

Systems, Matrices, and Determinants · Superchallenge problem

Positive real numbers xx, yy, zz satisfy

xy2z3=214,x2y3z=211,x3yz2=211.xy^2z^3=2^{14},\qquad x^2y^3z=2^{11},\qquad x^3yz^2=2^{11}.

Find x+y+zx+y+z.