Question: Problems with Digits and evalf

Hi,

I want to evaluate an approximation of the solution of the equation eq1 in [0,1] using 4 digits.

In first try, when I first write Digits:=4,  this seems avoid the command fsolve to display the solution.

In second try, when I write evalf(fsolve(eq1,beta=0..1),4),  evalf seems avoid the command fsolve to display the solution.

In the final try, when I write  
> fsolve(eq1,beta=0..1):
> evalf(%,4);
I have the expected result  0.5078.

Can you give me explications about the first and second results displayed by MAPLE 15?

Kind regards,

Alain Le Stang, France.
 

> restart;
> Digits:=4:
> K1:=1.45*10^(-4); p0:=10^5;p:=200*10^5;
> eq1:=K1=((16*beta^2*(2-beta)^2)/(27*(1-beta)^4))*(p0/p)^2;
> sol2:=fsolve(eq1,beta=0..1);

                           K1 := 0.0001450


                             p0 := 100000


                            p := 20000000


                                                     2             2
                                              beta  (2 - beta)
                 eq1 := 0.0001450 = -----------------
                                                    4
                                    67500 (1 - beta)


                                    2           2
                                beta  (2 - beta)
     sol2 := fsolve(0.0001450 = -----------------, beta, 0 .. 1)
                                                4
                                67500 (1 - beta)

> restart;
> K1:=1.45*10^(-4); p0:=10^5;p:=200*10^5;
> eq1:=K1=((16*beta^2*(2-beta)^2)/(27*(1-beta)^4))*(p0/p)^2;
> sol2:=evalf(fsolve(eq1,beta=0..1),4);

                        K1 := 0.0001450000000


                             p0 := 100000


                            p := 20000000


                                           2           2
                                       beta  (2 - beta)
              eq1 := 0.0001450000000 = -----------------
                                                       4
                                       67500 (1 - beta)


                                       2           2
                                   beta  (2 - beta)
  sol2 := fsolve(0.0001450000000 = -----------------, beta, 0 .. 1)
                                                   4
                                   67500 (1 - beta)

> restart;
> K1:=1.45*10^(-4); p0:=10^5;p:=200*10^5;
> eq1:=K1=((16*beta^2*(2-beta)^2)/(27*(1-beta)^4))*(p0/p)^2;
> fsolve(eq1,beta=0..1):
> evalf(%,4);
>

                        K1 := 0.0001450000000


                             p0 := 100000


                            p := 20000000


                                           2           2
                                       beta  (2 - beta)
              eq1 := 0.0001450000000 = -----------------
                                                       4
                                       67500 (1 - beta)


                                0.5078

 

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