2014 AMC 10A Problems/Problem 7
Contents
[hide]Problem
Nonzero real numbers , , , and satisfy and . How many of the following inequalities must be true?
Solution
Let us denote where and where . We can write that .
It is important to note that counterexample fully disproves a claim. Let's try substituting .
states that .Therefore, is false.
states that . Therefore, is false.
states that . Therefore, is false.
One of our four inequalities is true, hence, our answer is
~MathFun1000
Video Solution
~savannahsolver
See Also
2014 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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