Difference between revisions of "1961 AHSME Problems/Problem 7"
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Latest revision as of 20:09, 17 May 2018
Problem
When simplified, the third term in the expansion of 
is:
Solution
By the Binomial Theorem, the third term in the expansion is
![\[\binom{6}{2}(\frac{a}{\sqrt{x}})^{4}(\frac{-\sqrt{x}}{a^2})^2\]](http://latex.artofproblemsolving.com/2/7/d/27d86fc1cba7609d65121e51bb46b028a63758a3.png)
![\[15 \cdot \frac{a^4}{x^2} \cdot \frac{x}{a^4}\]](http://latex.artofproblemsolving.com/b/0/b/b0bc7984fb145b91aaaf4e4756a3a5ae7af8b35a.png)
![\[\frac{15}{x}\]](http://latex.artofproblemsolving.com/d/2/a/d2ad80dbbf439ad927a7a0d25453f342332c5f74.png)
The answer is 
.
See Also
| 1961 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
