Difference between revisions of "1955 AHSME Problems/Problem 42"
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== Solution == | == Solution == | ||
− | + | a+b/c = a^2(b/c) | |
+ | a= a^2(b/c) - b/c | ||
+ | a=(b/c)(a^2-1) | ||
+ | a/(a^2-1) = b/c | ||
+ | (a^2-1)b/a = c | ||
== See Also == | == See Also == |
Revision as of 23:17, 25 August 2021
Problem
If , and are positive integers, the radicals and are equal when and only when:
Solution
a+b/c = a^2(b/c) a= a^2(b/c) - b/c a=(b/c)(a^2-1) a/(a^2-1) = b/c (a^2-1)b/a = c
See Also
1955 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 41 |
Followed by Problem 43 | |
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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.