Difference between revisions of "2021 AMC 12A Problems/Problem 2"
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Revision as of 22:09, 11 February 2021
Contents
[hide]Problem
Under what conditions does hold, where and are real numbers?
It is never true.
It is true if and only if .
It is true if and only if .
It is true if and only if and .
It is always true.
Solution
Square both sides to get . Then, . Then, the answer is . Consider a right triangle with legs and and hypotenuse . Then one of the legs must be equal to , but they are also nonnegative as they are lengths. Therefore, both and are correct.
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
Video Solution by OmegaLearn (Using logic and analyzing answer choices)
~ pi_is_3.14
See also
2021 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 1 |
Followed by Problem 3 |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.