Determine all possible real x that satisfy this equation:
(1/x)x = 4x+1/16
I'm not sure whether there is another actual solution but the LHS (1/x)^x is defined for negative rational numbers with an odd denominator.
The RHS is always positive, so the rational solution would also have an even numerator.
By graphing |x|^(-x) you can get a better idea of what's going on. The crosses the RHS according to Desmos at around -0.3261
https://www.desmos.com/calculator/prvzcru2ut
A pretty good approximation of this decimal is -14/43 which you can see is pretty close to a solution.
If the actual solution is irrational, we can get arbitrarily close to it in this manner. I doubt there is an exact rational form as for the positive soltuons.
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Posted by Jer
on 2023-10-15 12:24:30 |
another solution?
