# solve function give a wrong solution

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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!
KSSV on 23 Jul 2020
Why do you think is wrong?

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.
Sorry I understood...the solutions are correct!

John D'Errico on 23 Jul 2020
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.