2023 AMC 12A Problems/Problem 23
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Contents
Problem
How many ordered pairs of positive real numbers satisfy the equation
Solution 1: AM-GM Inequality
Using AM-GM on the two terms in each factor on the left, we get meaning the equality condition must be satisfied. This means , so we only have solution.
Solution 2: Sum Of Squares
Equation is equivalent to where , . Therefore , so . Hence the answer is .
Video Solution 1 by OmegaLearn
Video Solution by MOP 2024
~r00tsOfUnity
Video Solution
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
See also
2023 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 22 |
Followed by Problem 24 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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