1991 AMC 12 Problem 27
Attempt Problem 27 of the 1991 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1991 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
If then
Answer: C
Small hint:
Rationalize
Big hint:
The last two terms of the requested expression are conjugates
Solution:
Because the given equation implies Its reciprocal is so adding yields and Also Therefore the requested expression is
Thus the correct answer is C.
Problem 27 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
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