Why the answer is like that?

syms x
s = vpa(solve((0.5)==(log(5)*log10(8)*sinh(x))/(atan(0.5)*(3^(1/5))*abs(cos(2*pi/3))*exp(cos(2*pi/3))),x))

the correct result of this equation is 0,06 but when i run this command matlab gives me this

s =

                                          0.060219526083180976165227748603359
   - 0.060219526083180976165227748603359 + 3.1415926535897932384626433832795i

So, why i found this result and how can i found just " 0,06 " ?

Thank you

Answer 1

[Walter Roberson]

0.06 is not a solution to that equation. If you substitute 0.06 for x you get

0.5 == 0.49817509413836472619769716883263

which is false.

The exact solution is asinh((3^(1/5)*atan(1/2)*exp(-1/2)*log(10))/(4*log(5)*log(8)))

[Jan]

@Walter: I opened this thread 20 minutes ago. To this time I did not see your answer, also you have posted it 16 minutes earlier. Do you observe such delays also?

It looks awkward that I have repeated your answer, but I did not see it.

Answer 2

[Jan]

No, 0.06 is not a solution. Simply try it:

x = 0.06
(log(5)*log10(8)*sinh(x)) / (atan(0.5)*(3^(1/5))*abs(cos(2*pi/3))*exp(cos(2*pi/3)))

This is 0.498175094138365, and not 0.5 .

But the shown results match the equation. So please explain, why you assume that 0.06 is a solution. This assumption is the problem to be solved.

Answer 3

[Sam Oznc]

First thank you for your answers i am really pleased.

This is tutorial question and yes i know, real answer is not 0.06 but question want to the answer with only 2 digit form(i think "format bank" command doing this), so it is 0.06 but i didnt ask that.

My question is why i found this answer and how i can find the correct answer with only two digit (like 0.xx) ?

s =
                                          0.060219526083180976165227748603359
   - 0.060219526083180976165227748603359 + 3.1415926535897932384626433832795i

[Walter Roberson]

vpa(s,2)

[Sam Oznc]

That's cool. Thank you