Difference between revisions of "1970 AHSME Problems/Problem 5"
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== Problem == | == Problem == | ||
| − | If <math>f(x)=\frac{x^4+x^2}{x+1}</math>, then <math>f( | + | If <math>f(x)=\frac{x^4+x^2}{x+1}</math>, then <math>f(i)</math>, where <math>i=\sqrt{-1}</math>, is equal to |
<math>\text{(A) } 1+i\quad | <math>\text{(A) } 1+i\quad | ||
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== Solution == | == Solution == | ||
| − | <math>\fbox{D}</math> | + | <math>i^4 = 1</math> and <math>i^2=-1</math>, so the numerator is <math>0</math>. As long as the denominator is not <math>0</math>, which it isn't, the answer is <math>0 \Rightarrow</math> <math>\fbox{D}</math> |
== See also == | == See also == | ||
| − | {{AHSME box|year=1970|num-b=4|num-a=6}} | + | {{AHSME 35p box|year=1970|num-b=4|num-a=6}} |
[[Category: Introductory Algebra Problems]] | [[Category: Introductory Algebra Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 01:06, 12 March 2017
Problem
If 
, then 
, where 
, is equal to
Solution
and 
, so the numerator is 
. As long as the denominator is not , which it isn't, the answer is 
See also
| 1970 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
