olymmath

JBMO-SL 2009 A2

  • Answer

Find the maximum value of z+xz+x, if (x,y,z,t)(x, y, z, t) satisfies the conditions:

{x2+y2=4z2+t2=9xt+yz≥6\left\{\begin{array}{l} x^{2}+y^{2}=4 \\ z^{2}+t^{2}=9 \\ x t+y z \geq 6 \end{array}\right.

Dataset text NuminaMath olympiads. Quoted with source.

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\sqrt{13}

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