1964 AHSME Problems/Problem 27
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Problem
If is a real number and where , then:
Solution
Let be point on a number line, and let be point . Let be a mobile point at . Geometrically, represents . If is between and , then . Otherwise, if is to the left of , then , which is greater than . If is to the right of , we have .
In all cases, the minimum value of is . Thus, will always be true if . If , it can be false for . If , then is always false because the LHS is too big.
Thus, the answer is .
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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All AHSME Problems and Solutions |
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