# Solve a nonlinear equation

Posted 8 years ago
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 Hi everyone, I wanna to solve the equation below. Could you please show me how I can write the commands in the Mathematica. Thank you in advance,The equation is : NSolve[x^5 - A[i]*x - 1 ==0,x] where A[i] = i/10, {i=1,10,1]
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Posted 8 years ago
 In[1]:= A[i_] := i/10In[6]:= Table[{A[i], x /. NSolve[x^5 - 2 A[i]*x - 1 == 0, x, Reals][[1]]}, {i, 1, 10}]Out[6]= {{1/10, 1.03846}, {1/5, 1.0741}, {3/10, 1.10726}, {2/5, 1.13824}, {1/2, 1.1673}, {3/5, 1.19468}, {7/10, 1.22055}, {4/5, 1.24508}, {9/10, -0.918257}, {1, -1.}}
Posted 8 years ago
 Dear,Could you show me how I can write the solution under format: {x[1], x[2], x[3], x[4], x[5]} after solving the following equationThank you in advanceA[i_] := i/10Table[NSolve[x^5 - A[i]x/ - 1 == 0, x, Reals], {i, 1, 5}]The results are:{{{x -> 1.01961}}, {{x -> 1.03846}}, {{x -> 1.05661}}, {{x -> 1.0741}}, {{x -> 1.09097}}} But I want to write only {1.01961, 1.03846, 1.05661, 1.0741, 1.09097} to faciliate the copy and paste in excel
Posted 8 years ago
 But Is it possible to write x[i] as a table like [x[1],x[2],...,x[5]]. Because actually it gives: {{{x -> 1.01961}}, {{x -> 1.03846}}, {{x -> 1.05661}}, {{x -> 1.0741}}, {{x -> 1.09097}}}I wanna only :{1.01961,1.03846,1.05661,1.0741,1.09097} Thank you in advance,
Posted 8 years ago
 You can modify the Table command: Table[{A[i], NSolve[x^5 - 2 x/5 - 1 == 0, x, Reals]}, {i, 1, 5}] 
Posted 8 years ago
 You are using "A" as a variable name. I strongly suggest changing the name of it. Single letter variable or function names are a bad idea. The error message is complaining that "A" is already defined. Try running your code in a clean kernel. That is, run Quit and then try running the code.
Posted 8 years ago
 It works :). Thank you very much. After, Is it possible to print x[i] and A[i] by two colones as?A[1] x[1] A[2] x[2] .... A[10] x[10]
Posted 8 years ago
 First, define the function "A". I strongly recommend creating more expressive names than this. A[i_] := i/10 Use Table to create a list of functions Table[x^5 - A[i]*x - 1 == 0, {i, 1 , 10}] Tables like this can be used with NSolve. The set of equations may or may not have a solution.
Posted 8 years ago
 Dear Sean Clarke,According to your help, I wrote the following commands but I think it does not work. Can you explain me please.(Debug) In[28]:= NSolve[x^5 - x/10 - 1 == 0, x, Reals](Debug) Out[28]= {{x -> 1.01961}}(Debug) In[29]:= NSolve[x^5 - x/5 - 1 == 0, x, Reals](Debug) Out[29]= {{x -> 1.03846}}(Debug) In[30]:= NSolve[x^5 - 3 x/10 - 1 == 0, x, Reals](Debug) Out[30]= {{x -> 1.05661}}(Debug) In[31]:= NSolve[x^5 - 2 x/5 - 1 == 0, x, Reals](Debug) Out[31]= {{x -> 1.0741}}(Debug) In[43]:= Clear[x];A[i_] := i/10; Table[NSolve[x^5 - 2 x/5 - 1 == 0, x, Reals], {i, 1, 5}](Debug) During evaluation of In[43]:= SetDelayed::write: Tag List in {1/10,1/5,3/10,2/5,1/2,3/5,7/10,4/5,9/10,1}[i_] is Protected. >>(Debug) Out[45]= {{{x -> 1.0741}}, {{x -> 1.0741}}, {{x -> 1.0741}}, {{x -> 1.0741}}, {{x -> 1.0741}}}
Posted 8 years ago
 In[13]:= a = Range[10]/10 Out[13]= {1/10, 1/5, 3/10, 2/5, 1/2, 3/5, 7/10, 4/5, 9/10, 1} In[14]:= Table[NSolve[x^5 - a[[i]]*x - 1 == 0, x], {i, 10}] Out[14]= {{{x -> -0.802967 - 0.568379 I}, {x -> -0.802967 + 0.568379 I}, {x -> 0.293163 - 0.96304 I}, {x -> 0.293163 + 0.96304 I}, {x -> 1.01961}}, {{x -> -0.797202 - 0.548183 I}, {x -> -0.797202 + 0.548183 I}, {x -> 0.27797 - 0.975447 I}, {x -> 0.27797 + 0.975447 I}, {x -> 1.03846}}, {{x -> -0.79176 - 0.527168 I}, {x -> -0.79176 + 0.527168 I}, {x -> 0.263454 - 0.988232 I}, {x -> 0.263454 + 0.988232 I}, {x -> 1.05661}}, {{x -> -0.786675 - 0.5053 I}, {x -> -0.786675 + 0.5053 I}, {x -> 0.249625 - 1.00134 I}, {x -> 0.249625 + 1.00134 I}, {x -> 1.0741}}, {{x -> -0.781977 - 0.482538 I}, {x -> -0.781977 + 0.482538 I}, {x -> 0.236492 - 1.01473 I}, {x -> 0.236492 + 1.01473 I}, {x -> 1.09097}}, {{x -> -0.77769 - 0.458827 I}, {x -> -0.77769 + 0.458827 I}, {x -> 0.22406 - 1.02834 I}, {x -> 0.22406 + 1.02834 I}, {x -> 1.10726}}, {{x -> -0.77383 - 0.434095 I}, {x -> -0.77383 + 0.434095 I}, {x -> 0.212328 - 1.04213 I}, {x -> 0.212328 + 1.04213 I}, {x -> 1.123}}, {{x -> -0.770409 - 0.408237 I}, {x -> -0.770409 + 0.408237 I}, {x -> 0.201289 - 1.05602 I}, {x -> 0.201289 + 1.05602 I}, {x -> 1.13824}}, {{x -> -0.767428 - 0.381103 I}, {x -> -0.767428 + 0.381103 I}, {x -> 0.19093 - 1.06998 I}, {x -> 0.19093 + 1.06998 I}, {x -> 1.153}}, {{x -> -0.764884 - 0.352472 I}, {x -> -0.764884 + 0.352472 I}, {x -> 0.181232 - 1.08395 I}, {x -> 0.181232 + 1.08395 I}, {x -> 1.1673}}}