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Real Number Resolution 2 (Posted on 2015-10-27) Difficulty: 3 of 5
Find all possible values of a real number X that satisfies this equation:

2X + 3X + 6X = X2

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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Solution proposed solution Comment 1 of 1
-1 is a solution, and, to put it another way,

2^x + 3^x + 6^x - x^2 = 0,   for x = -1

The function on the LHS has derivative

ln(2)2^x + ln(3)3^x+ln(6)6^x - 2x

which, at x=-1, equals approximately  3.011404264707352, which is positive, and in fact is everywhere positive, as can be seen by graphing, so x=-1 is the only solution.

  Posted by Charlie on 2015-10-27 16:00:01
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