solve function give a wrong solution

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]

Why do you think is wrong?

Answer 1

[Vladimir Sovkov]

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.

[Adriano]

Sorry I understood...the solutions are correct!

Answer 2

[John D'Errico]

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.