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[example,solve]

Run Example
(%i1)example(solve);

(%i1) 
(%i2) solve(asin(cos(3*x))*(f(x)-1),x)

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
                                   %pi
(%o2)                         [x = ---, f(x) = 1]
                                    6
(%i1) 
(%i3) ev(solve(5^f(x) = 125,f(x)),solveradcan)
                                       log(125)
(%o3)                          [f(x) = --------]
                                        log(5)
(%i1) 
(%i4) [4*x^2-y^2 = 12,x*y-x = 2]
                             2    2
(%o4)                    [4 x  - y  = 12, x y - x = 2]
(%i1) 
(%i5) solve(%,[x,y])
(%o5) [[x = 2, y = 2], [x = 0.5202594388652 %i - 0.13312403573587, 
y = 0.076783785237878 - 3.608003221870287 %i], 
[x = - 0.5202594388652 %i - 0.13312403573587, 
y = 3.608003221870287 %i + 0.076783785237878], 
[x = - 1.733751846381093, y = - 0.15356757100197]]
(%i1) 
(%i6) solve(1+a*x+x^3,x)
                                       3
              sqrt(3) %i   1   sqrt(4 a  + 27)   1 1/3
(%o6) [x = (- ---------- - -) (--------------- - -)
                  2        2          3/2        2
                                   2 3
        sqrt(3) %i   1
       (---------- - -) a                                    3
            2        2              sqrt(3) %i   1   sqrt(4 a  + 27)   1 1/3
 - --------------------------, x = (---------- - -) (--------------- - -)
              3                         2        2          3/2        2
      sqrt(4 a  + 27)   1 1/3                            2 3
   3 (--------------- - -)
             3/2        2
          2 3
         sqrt(3) %i   1
      (- ---------- - -) a                  3
             2        2             sqrt(4 a  + 27)   1 1/3
 - --------------------------, x = (--------------- - -)
              3                            3/2        2
      sqrt(4 a  + 27)   1 1/3           2 3
   3 (--------------- - -)
             3/2        2
          2 3
               a
 - --------------------------]
              3
      sqrt(4 a  + 27)   1 1/3
   3 (--------------- - -)
             3/2        2
          2 3
(%i1) 
(%i7) solve(x^3-1)
                    sqrt(3) %i - 1        sqrt(3) %i + 1
(%o7)          [x = --------------, x = - --------------, x = 1]
                          2                     2
(%i1) 
(%i8) solve(x^6-1)
           sqrt(3) %i + 1      sqrt(3) %i - 1                 sqrt(3) %i + 1
(%o8) [x = --------------, x = --------------, x = - 1, x = - --------------, 
                 2                   2                              2
                                                         sqrt(3) %i - 1
                                                   x = - --------------, x = 1]
                                                               2
(%i1) 
(%i9) ev(x^6-1,%[1])
                                             6
                             (sqrt(3) %i + 1)
(%o9)                        ----------------- - 1
                                    64
(%i1) 
(%i10) expand(%)
(%o10)                                 0
(%i1) 
(%i11) x^2-1
                                     2
(%o11)                              x  - 1
(%i1) 
(%i12) solve(%,x)
(%o12)                         [x = - 1, x = 1]
(%i1) 
(%i13) ev(%th(2),%[1])
(%o13)                                 0
(%o13)                               done
(%i14) 
Run Example
eq1: 2*x+y+3*z=10;
(%o1)                         3 z + y + 2 x = 10
(%i2) eq2: x+y+z=6;
(%o2)                            z + y + x = 6
(%i3) eq3: x+3*y+2*z=13;
(%o3)                         2 z + 3 y + x = 13
(%i4) solve([eq1,eq2,eq3]);
(%o4)                       [[z = 1, y = 3, x = 2]]
(%i5) example(solve);

(%i1) 
(%i6) solve(asin(cos(3*x))*(f(x)-1),x)

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
                                   %pi
(%o6)                         [x = ---, f(x) = 1]
                                    6
(%i1) 
(%i7) ev(solve(5^f(x) = 125,f(x)),solveradcan)
                                       log(125)
(%o7)                          [f(x) = --------]
                                        log(5)
(%i1) 
(%i8) [4*x^2-y^2 = 12,x*y-x = 2]
                             2    2
(%o8)                    [4 x  - y  = 12, x y - x = 2]
(%i1) 
(%i9) solve(%,[x,y])
(%o9) [[x = 2, y = 2], [x = 0.5202594388652 %i - 0.13312403573587, 
y = 0.076783785237878 - 3.608003221870287 %i], 
[x = - 0.5202594388652 %i - 0.13312403573587, 
y = 3.608003221870287 %i + 0.076783785237878], 
[x = - 1.733751846381093, y = - 0.15356757100197]]
(%i1) 
(%i10) solve(1+a*x+x^3,x)
                                        3
               sqrt(3) %i   1   sqrt(4 a  + 27)   1 1/3
(%o10) [x = (- ---------- - -) (--------------- - -)
                   2        2          3/2        2
                                    2 3
        sqrt(3) %i   1
       (---------- - -) a                                    3
            2        2              sqrt(3) %i   1   sqrt(4 a  + 27)   1 1/3
 - --------------------------, x = (---------- - -) (--------------- - -)
              3                         2        2          3/2        2
      sqrt(4 a  + 27)   1 1/3                            2 3
   3 (--------------- - -)
             3/2        2
          2 3
         sqrt(3) %i   1
      (- ---------- - -) a                  3
             2        2             sqrt(4 a  + 27)   1 1/3
 - --------------------------, x = (--------------- - -)
              3                            3/2        2
      sqrt(4 a  + 27)   1 1/3           2 3
   3 (--------------- - -)
             3/2        2
          2 3
               a
 - --------------------------]
              3
      sqrt(4 a  + 27)   1 1/3
   3 (--------------- - -)
             3/2        2
          2 3
(%i1) 
(%i11) solve(x^3-1)
                    sqrt(3) %i - 1        sqrt(3) %i + 1
(%o11)         [x = --------------, x = - --------------, x = 1]
                          2                     2
(%i1) 
(%i12) solve(x^6-1)
            sqrt(3) %i + 1      sqrt(3) %i - 1                 sqrt(3) %i + 1
(%o12) [x = --------------, x = --------------, x = - 1, x = - --------------, 
                  2                   2                              2
                                                         sqrt(3) %i - 1
                                                   x = - --------------, x = 1]
                                                               2
(%i1) 
(%i13) ev(x^6-1,%[1])
                                             6
                             (sqrt(3) %i + 1)
(%o13)                       ----------------- - 1
                                    64
(%i1) 
(%i14) expand(%)
(%o14)                                 0
(%i1) 
(%i15) x^2-1
                                     2
(%o15)                              x  - 1
(%i1) 
(%i16) solve(%,x)
(%o16)                         [x = - 1, x = 1]
(%i1) 
(%i17) ev(%th(2),%[1])
(%o17)                                 0
(%o17)                               done
(%i18) 

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