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MATH / Let x, y, and z be positive real numbers such that

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let x,x, y,y, and zz be positive real numbers such that 1x4+1y4+1z4=1.\frac{1}{x^4} + \frac{1}{y^4} + \frac{1}{z^4} = 1.Find the minimum value of x4y4+x4z4+y4z4x3y2z3.\frac{x^4 y^4 + x^4 z^4 + y^4 z^4}{x^3 y^2 z^3}.
Plain-text mathematical notation (without MathML)
Let x, y, and z be positive real numbers such that
(1)/(x⁴)+(1)/(y⁴)+(1)/(z⁴)=1.Find the minimum value of
(x⁴y⁴+x⁴z⁴+y⁴z⁴)/(x³y²z³).
Original LaTeX notation
Let $x,$ $y,$ and $z$ be positive real numbers such that
\[\frac{1}{x^4} + \frac{1}{y^4} + \frac{1}{z^4} = 1.\]Find the minimum value of
\[\frac{x^4 y^4 + x^4 z^4 + y^4 z^4}{x^3 y^2 z^3}.\]

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
f62e6cc9-8389-58cf-b537-5b16769d9700
task_key
intermediate~5falgebra--test--f62e6cc9-8389-58cf-b537-5b16769d9700
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import