Difference between revisions of "2022 AMC 10A Problems/Problem 11"
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Note that <math>m=3</math> or <math>m=4</math> from the quadratic equation above. | Note that <math>m=3</math> or <math>m=4</math> from the quadratic equation above. | ||
− | ~MRENTHUSIASM ~KingRavi | + | ~MRENTHUSIASM |
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+ | ~KingRavi | ||
==Video Solution 1 (Quick and Easy)== | ==Video Solution 1 (Quick and Easy)== |
Revision as of 15:48, 12 November 2022
Problem
Ted mistakenly wrote as
What is the sum of all real numbers
for which these two expressions have the same value?
Solution
We are given that
Converting everything into powers of
we have
We multiply both sides by
, then rearrange as
By Vieta's Formulas, the sum of such values of
is
Note that or
from the quadratic equation above.
~MRENTHUSIASM
~KingRavi
Video Solution 1 (Quick and Easy)
~Education, the Study of Everything
See Also
2022 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.