1956 AMC 12 Problem 41
Attempt Problem 41 of the 1956 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 1956 AMC 12 solutions, or check the answer key.
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41.
The equation where is satisfied by:
no value of
all values of
only
all integral values of only
all rational values of only
Answer: C
Small hint:
Substitute on both sides before expanding
Big hint:
The and constant terms cancel
Solution:
Substituting gives Cancelling the common quadratic and constant terms leaves so This value satisfies both equations.
Thus, the correct answer is C.