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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_23 / How many ordered pairs of positive real numbers (a,b) satisfy the equation

Problem

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problem

How many ordered pairs of positive real numbers

(a,b)

satisfy the equation \[(1+2a)(2+2b)(2a+b) = 32ab?\]

Plain-text mathematical notation (without MathML)

How many ordered pairs of positive real numbers (a,b) satisfy the equation
\[(1+2a)(2+2b)(2a+b) = 32ab?\]

Original LaTeX notation

How many ordered pairs of positive real numbers $(a,b)$ satisfy the equation
\[(1+2a)(2+2b)(2a+b) = 32ab?\]

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_23
task_id: 1262875f-5d43-5f7f-9932-be130dfd0b35
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f23
task_revision_id: 2
config / split: default / train

Official source

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