2013 AMC 8 Problems/Problem 15
Contents
Problem
If , , and , what is the product of , , and ?
Video Solution by OmegaLearn
https://youtu.be/7an5wU9Q5hk?t=301
~ pi_is_3.14
Video Solution 2
https://youtu.be/ew7QnjAAHcw ~savannahsolver
Solution
Solution 1: Solving
First, we're going to solve for . Start with . Then, change to . Subtract from both sides to get and see that is . Now, solve for . Since , must equal , so . Now, solve for . can be simplified to which simplifies further to . Therefore, . equals which equals . So, the answer is .
Solution 2: Process of Elimination
First, we solve for . As Solution 1 perfectly states, can be simplified to which simplifies further to . Therefore, . We know that you cannot take a root of any of the numbers raised to , , or and get a rational answer, and none of the answer choices are irrational, so that rules out the possibility that , , or is a fraction. The only answer choice that is divisible by is .
See Also
2013 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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All AJHSME/AMC 8 Problems and Solutions |
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