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[?] What do these solutions from Solve mean?

Posted 8 years ago

When I compute the following (with Mathematica 11.2):

Solve[(1 + r)^81 == 1.45, r]

I get a long list of solutions, all negative reals and complex numbers, apart from the one positive real answer I was expecting.

The solution list begins...

{{r -> -4.46763}, {r -> -4.45283}, {r -> -4.30803}, {r -> -4.11268}, {r -> -3.94294}....etc.

These values of r do not even remotely solve the equation, as far as I can see. Apart from anything else, they make the LHS negative, so it cannot be equal to the RHS, which is positive.

What is the meaning of these solutions? Is this just a bug in Mathematica? Or is there some sense in which they are solutions?

POSTED BY: Marc Widdowson
6 Replies

What about 1 + r = x; x^81 == 1.45 , so

In[16]:= x = N[Power[1.45`30, (81)^-1], 30]

Out[16]= 1.00459774172863829263717967674

and then r = x - 1

POSTED BY: Hans Dolhaine
Posted 8 years ago

Some further observations

Solve[(1 + r)^n == C, r]

gives n solutions. E.g. there are 81 solutions in the example above.

Solve[(1 + r)^4 == 1, r]

gives

{{r -> -2}, {r -> -1 - i}, {r -> -1 + i}, {r -> 0}}

which are in fact all valid solutions, in this case.

POSTED BY: Marc Widdowson
Posted 8 years ago
POSTED BY: Marc Widdowson
POSTED BY: Sander Huisman
Posted 8 years ago
POSTED BY: Marc Widdowson
POSTED BY: Claude Mante
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