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polynomial problem 2 (Posted on 2016-09-30) Difficulty: 2 of 5
f(x) is a polynomial satisfying the condition below.

f(x)f(1/x) = f(x) + f(1/x)

If f(10) = 1001, find f(20).

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

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Solution Solution (spoiler) Comment 1 of 1
If f(10) = 1001,
then 1001*f(1/10) = 1001 + f(1/10).
Solving, f(1/10) = 1001/1000 = 1 + 1/1000.

f(x) could be as simple as x^3 + 1, and that function does satisfy the the first required property.  In fact, any function of the form f(x) = x^y + 1 has the first required property. 

so f(20) = 8001.  Final answer.


Edited on October 1, 2016, 12:51 pm
  Posted by Steve Herman on 2016-10-01 11:09:00

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