solve function give a wrong solution

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Adriano
Adriano on 23 Jul 2020
Answered: John D'Errico on 23 Jul 2020
Hi all,
I'm trying to solve a simple equation in Matlab using solve function. The code is:
syms x
solv = solve( (1+x/12)^12 == 1.02)
The solution is 0.0204 however Matalb give me this solution:
solv =
- (6*50^(11/12)*51^(1/12))/25 - 12
(6*50^(11/12)*51^(1/12))/25 - 12
- (50^(11/12)*51^(1/12)*6i)/25 - 12
(50^(11/12)*51^(1/12)*6i)/25 - 12
- (6*50^(11/12)*51^(1/12)*(3^(1/2)/2 - 1i/2))/25 - 12
(6*50^(11/12)*51^(1/12)*(3^(1/2)/2 - 1i/2))/25 - 12
- (6*50^(11/12)*51^(1/12)*(3^(1/2)/2 + 1i/2))/25 - 12
(6*50^(11/12)*51^(1/12)*(3^(1/2)/2 + 1i/2))/25 - 12
- (6*50^(11/12)*51^(1/12)*((3^(1/2)*1i)/2 - 1/2))/25 - 12
(6*50^(11/12)*51^(1/12)*((3^(1/2)*1i)/2 - 1/2))/25 - 12
- (6*50^(11/12)*51^(1/12)*((3^(1/2)*1i)/2 + 1/2))/25 - 12
(6*50^(11/12)*51^(1/12)*((3^(1/2)*1i)/2 + 1/2))/25 - 12
>> round(solv)
ans =
-24
0
- 12 - 12i
- 12 + 12i
- 22 + 6i
- 2 - 6i
- 22 - 6i
- 2 + 6i
- 6 - 10i
- 18 + 10i
- 18 - 10i
- 6 + 10i
Why it happen? Someone can help me? Thanks!

Accepted Answer

Vladimir Sovkov
Vladimir Sovkov on 23 Jul 2020
Edited: Vladimir Sovkov on 23 Jul 2020
syms x
solv = double(solve( (1+x/12)^12 == 1.02))
There are many solutions. The one you are interested in is rather 0.0198189756230421 but not 0.0204.
  1 Comment
Adriano
Adriano on 23 Jul 2020
Sorry I understood...the solutions are correct!

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More Answers (1)

John D'Errico
John D'Errico on 23 Jul 2020
Just an addendum, though the answer by @Vladimir Sovkov is correct.
Using round to convert those results is wrong. Instead use either double or vpa to do so, depending on whether you want a symbolic or double precision answer. Thus we see:
digits 20
>> vpa(solv)
ans =
-24.019818975623042098
0.019818975623042097611
- 12.0 - 12.019818975623042098i
- 12.0 + 12.019818975623042098i
- 22.40946858177980274 + 6.0099094878115210488i
- 1.5905314182201972597 - 6.0099094878115210488i
- 22.40946858177980274 - 6.0099094878115210488i
- 1.5905314182201972597 + 6.0099094878115210488i
- 5.9900905121884789512 - 10.40946858177980274i
- 18.009909487811521049 + 10.40946858177980274i
- 18.009909487811521049 - 10.40946858177980274i
- 5.9900905121884789512 + 10.40946858177980274i
The second solution is apparently the one you wanted, as has already been shown.

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