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Omni-MATH / x, y and z are positive reals such that x+y+z=xyz. Find the minimum value of: x⁷(yz−1)+y⁷(zx−1)+z⁷(xy−1)

Problem

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problem

x

y

and

z

are positive reals such that

x+y+z=xyz

. Find the minimum value of:

x^7(yz-1)+y^7(zx-1)+z^7(xy-1)

Plain-text mathematical notation (without MathML)

x, y and z are positive reals such that x+y+z=xyz. Find the minimum value of:
x⁷(yz−1)+y⁷(zx−1)+z⁷(xy−1)

Original LaTeX notation

$x$, $y$ and $z$ are positive reals such that $x+y+z=xyz$. Find the minimum value of:
\[ x^7(yz-1)+y^7(zx-1)+z^7(xy-1) \]

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task_id: 4f27e1b5-88e7-55c4-a2b3-9bcd1a41cbca
task_key: test--4f27e1b5-88e7-55c4-a2b3-9bcd1a41cbca
task_revision_id: 3
config / split: / test

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