1991 AHSME Problems/Problem 20
Problem
The sum of all real such that is
Solution
Note that so we let and The original equation becomes We expand the right side, then rearrange:
- If then from which
- If then from which
- If then As we rewrite this equation, then factor:
If then
If then there are no real solutions for as holds for all real numbers
Together, the answer is
~Hapaxoromenon (Solution)
~MRENTHUSIASM (Reformatting)
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.