2013 AMC 12A Problems/Problem 8
Contents
Problem
Given that and are distinct nonzero real numbers such that , what is ?
Solution 1
Since , we may assume that and/or, equivalently, .
Cross multiply in either equation, giving us .
Solution 2
Since
Solution 3
Let Consider the equation Reorganizing, we see that satisfies Notice that there can be at most two distinct values of which satisfy this equation, and and are two distinct possible values for Therefore, and are roots of this quadratic, and by Vieta’s formulas we see that thereby must equal
~ Professor-Mom
Video Solution
https://youtu.be/ba6w1OhXqOQ?t=1129
~ pi_is_3.14
Video Solution
https://youtu.be/CCjcMVtkVaQ ~sugar_rush
See also
2013 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
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All AMC 12 Problems and Solutions |
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