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Omni-MATH / Let x and y be non-negative real numbers that sum to 1. Compute the number of ordered pairs (a,b) with a,b∈{0,1,2,3,4} such that the expression x^(a)y^(b)+y^(a)x^(b) has maximum va…

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problem

Let xx and yy be non-negative real numbers that sum to 1. Compute the number of ordered pairs (a,b)(a, b) with a,b∈{0,1,2,3,4}a, b \in\{0,1,2,3,4\} such that the expression xayb+yaxbx^{a} y^{b}+y^{a} x^{b} has maximum value 21−a−b2^{1-a-b}.
Plain-text mathematical notation (without MathML)
Let x and y be non-negative real numbers that sum to 1. Compute the number of ordered pairs (a,b) with a,b∈{0,1,2,3,4} such that the expression x^(a)y^(b)+y^(a)x^(b) has maximum value 2^(1−a−b).
Original LaTeX notation
Let $x$ and $y$ be non-negative real numbers that sum to 1. Compute the number of ordered pairs $(a, b)$ with $a, b \in\{0,1,2,3,4\}$ such that the expression $x^{a} y^{b}+y^{a} x^{b}$ has maximum value $2^{1-a-b}$.

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Source and history

task_id
87710d44-2a9d-5a68-b665-a795ffc0de48
task_key
test--87710d44-2a9d-5a68-b665-a795ffc0de48
task_revision_id
1
config / split
/ test

Official source

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