Difference between revisions of "1997 AHSME Problems/Problem 3"
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Latest revision as of 13:12, 5 July 2013
Problem 3
If 
, 
, and 
are real numbers such that
,then 
Solution
If the sum of three squared expressions is zero, then each expression itself must be zero, since 
with the equality iff 
.
In this case, 
, 
, and 
. Adding the three equations and moving the constant to the right gives 
, and the answer is 
.
See also
| 1997 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
