1976 AHSME Problems/Problem 7
If is a real number, then the quantity is positive if and only if
Solution
We divide our solution into three cases: that of , that of , and that of . (When or , the expression is zero, therefore not positive.)
If , then the first factor is negative, and the second factor is also negative.
If , then the first factor is positive, and the second factor is also positive.
If , the first factor is negative, but the second factor is positive.
Combining this with the rules for signs and multiplication, we find that the expression is positive when or when , so our answer is and we are done.
See also
1976 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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