Difference between revisions of "1955 AHSME Problems/Problem 13"
Angrybird029 (talk | contribs) (Created page with "== Problem 13== The fraction <math>\frac{a^{-4}-b^{-4}}{a^{-2}-b^{-2}}</math> is equal to: <math> \textbf{(A)}\ a^{-6}-b^{-6}\qquad\textbf{(B)}\ a^{-2}-b^{-2}\qquad\textbf{...") |
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==Solution== | ==Solution== | ||
| − | By the difference of squares property, <math>a^{-4} - b^{-4}</math> is equivalent to <math>(a^{-2} + b^{-2})(a^{-2} - b^{-2})</math>. This means the fraction is now equal to <math>\frac{(a^{-2} + b^{-2})(a^{-2} - b^{-2})}{a^{-2} - b^{-2}}</math>, which simplifies to <math>\textbf{(C)}\ a^{-2}+b^{-2}</math> | + | By the difference of squares property, <math>a^{-4} - b^{-4}</math> is equivalent to <math>(a^{-2} + b^{-2})(a^{-2} - b^{-2})</math>. This means the fraction is now equal to <math>\frac{(a^{-2} + b^{-2})(a^{-2} - b^{-2})}{a^{-2} - b^{-2}}</math>, which simplifies to <math>\textbf{(C)}\ a^{-2}+b^{-2}</math> |
| + | == See Also == | ||
| + | {{AHSME box|year=1955|num-b=12|num-a=14}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Latest revision as of 12:23, 1 August 2020
Problem 13
The fraction 
is equal to:
Solution
By the difference of squares property, 
is equivalent to 
. This means the fraction is now equal to 
, which simplifies to 
See Also
| 1955 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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. 
