@pagan 

I follow you now, makes sense. 

Does it matter how many digits I print newsteadmod to? currently i have set 15.

Thanks :)

@pagan 

I follow you now, makes sense. 

Does it matter how many digits I print newsteadmod to? currently i have set 15.

Thanks :)

@pagan 

I dont quite follow you, being a new user to maple. Do you mind editing my code and showing me. I find I learn stuff better when I see the code, makes me understand it where I went wrong.

@pagan 

I dont quite follow you, being a new user to maple. Do you mind editing my code and showing me. I find I learn stuff better when I see the code, makes me understand it where I went wrong.

Ok here is the program now:

eq := 0.178e-1*x*tan(0.2e-4*sqrt(x))^2 = 0.232e13-x;

neweq := subs(x = 10^y, eq);

Digits := 15;

newans := Student:-Calculus1:-Roots(neweq, y = log[10](10^10) .. log[10](10^11));

newans2 := Student:-Calculus1:-Roots(simplify((rhs-lhs)(neweq)), y = log[10](10^10) .. log[10](10^11));

all := [op(evalf[14]({op(newans), op(newans2)}))];

Digits := 100;

allmod := map(proc (t) options operator, arrow; 10^t end proc, all);

Digits := 15; newestmod := evalf(allmod);

Digits := 100;

check := map(proc (t) options operator, arrow; eval((rhs-lhs)(eq), x = t) end proc, allmod);

Digits := 15; evalf(check);

Here is the output

                               
              [10.7405813131081, 10.7482811219187]
              [10.7405813131081, 10.7482811219186]
               [10.740581313108, 10.748281121919]
                           
         [5.50276939410435 x10^10  , 5.60120053883583x10^ 10  ]           {the solutions)

              [167.706091024260, 403.172634297628]    

 {the solutions plugged back in the equation to give these last two values, 

these should be zero}

As you can see I still have a problem, the so called solutions that are outputted dont seem to 

check out when plugged back in.

Thanks for replying guys. 

Ok here is the program now:

eq := 0.178e-1*x*tan(0.2e-4*sqrt(x))^2 = 0.232e13-x;

neweq := subs(x = 10^y, eq);

Digits := 15;

newans := Student:-Calculus1:-Roots(neweq, y = log[10](10^10) .. log[10](10^11));

newans2 := Student:-Calculus1:-Roots(simplify((rhs-lhs)(neweq)), y = log[10](10^10) .. log[10](10^11));

all := [op(evalf[14]({op(newans), op(newans2)}))];

Digits := 100;

allmod := map(proc (t) options operator, arrow; 10^t end proc, all);

Digits := 15; newestmod := evalf(allmod);

Digits := 100;

check := map(proc (t) options operator, arrow; eval((rhs-lhs)(eq), x = t) end proc, allmod);

Digits := 15; evalf(check);

Here is the output

                               
              [10.7405813131081, 10.7482811219187]
              [10.7405813131081, 10.7482811219186]
               [10.740581313108, 10.748281121919]
                           
         [5.50276939410435 x10^10  , 5.60120053883583x10^ 10  ]           {the solutions)

              [167.706091024260, 403.172634297628]    

 {the solutions plugged back in the equation to give these last two values, 

these should be zero}

As you can see I still have a problem, the so called solutions that are outputted dont seem to 

check out when plugged back in.

Thanks for replying guys. 

The program is now

eq := 0.178e-1*x*tan(0.2e-4*sqrt(x))^2 = 0.232e13-x;

neweq := subs(x = 10^y, eq);

Digits := 15;

newans := Student:-Calculus1:-Roots(neweq, y = log[10](10^10) .. log[10](2*10^12));

newans2 := Student:-Calculus1:-Roots(simplify((rhs-lhs)(neweq)), y = log[10](10^10) .. log[10](2*10^12));

all := [op(evalf[14]({op(newans), op(newans2)}))];

Digits := 100;

allmod := map(proc (t) options operator, arrow; 10^t end proc, all);

Digits := 15; newestmod := evalf(allmod);

Digits := 100;

check := map(proc (t) options operator, arrow; eval((rhs-lhs)(eq), x = t) end proc, allmod);

Digits := 15;

evalf(check)

the program should output the solutions and then check them by plugging them into the equation, to see if the equation is satisfied. 

A whole lot of values are outputted but the solution (that I know) are not.

The program is now

eq := 0.178e-1*x*tan(0.2e-4*sqrt(x))^2 = 0.232e13-x;

neweq := subs(x = 10^y, eq);

Digits := 15;

newans := Student:-Calculus1:-Roots(neweq, y = log[10](10^10) .. log[10](2*10^12));

newans2 := Student:-Calculus1:-Roots(simplify((rhs-lhs)(neweq)), y = log[10](10^10) .. log[10](2*10^12));

all := [op(evalf[14]({op(newans), op(newans2)}))];

Digits := 100;

allmod := map(proc (t) options operator, arrow; 10^t end proc, all);

Digits := 15; newestmod := evalf(allmod);

Digits := 100;

check := map(proc (t) options operator, arrow; eval((rhs-lhs)(eq), x = t) end proc, allmod);

Digits := 15;

evalf(check)

the program should output the solutions and then check them by plugging them into the equation, to see if the equation is satisfied. 

A whole lot of values are outputted but the solution (that I know) are not.

Yes thats correct.

Thanks so much pagan. I wish i was taught maple at university, it wasn't part of my course. Maple is a very useful program. 

Yes thats correct.

Thanks so much pagan. I wish i was taught maple at university, it wasn't part of my course. Maple is a very useful program. 

pagan your method is excellent! 

it agrees with almost all my answers when I use another method (much longer that requires plotting and searching for roots)

However i noticed that when you change your equation (only changed the underlined values) 

restart:
eq:=tan(4*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))
    /tan(4*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))
  = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12
    /(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2:

to the quation

restart:
eq:=tan(6*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))
    /tan(6*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))
  = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12
    /(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2:

I get values from your method:

[8.23681389099981*10^5, 1.63071661915857*10^6, 1.83601970432122*10^6]

when my values (from my method) are:

one value of yours is incorrect here

pagan your method is excellent! 

it agrees with almost all my answers when I use another method (much longer that requires plotting and searching for roots)

However i noticed that when you change your equation (only changed the underlined values) 

restart:
eq:=tan(4*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))
    /tan(4*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))
  = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12
    /(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2:

to the quation

restart:
eq:=tan(6*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))
    /tan(6*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))
  = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12
    /(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2:

I get values from your method:

[8.23681389099981*10^5, 1.63071661915857*10^6, 1.83601970432122*10^6]

when my values (from my method) are:

one value of yours is incorrect here

ok so the task doesnt work for irrationals?, thats a shame because solutions are always irrational to that equation.

I have also tried 

tan(2*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))/tan(2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2)) = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2;

lhs(%)-rhs(%);

EQ := subs(x^2 = z, %);

RootOf(%, z);

z0 := allvalues(%);

sqrt(%);

evalf(%)

Each time i change the bolded 2 in the top equation to another value, say 3, i get the same answer. So is it because it only works for rationals and not irrationals?

Thankyou very much for the help. 

ok so the task doesnt work for irrationals?, thats a shame because solutions are always irrational to that equation.

I have also tried 

tan(2*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))/tan(2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2)) = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2;

lhs(%)-rhs(%);

EQ := subs(x^2 = z, %);

RootOf(%, z);

z0 := allvalues(%);

sqrt(%);

evalf(%)

Each time i change the bolded 2 in the top equation to another value, say 3, i get the same answer. So is it because it only works for rationals and not irrationals?

Thankyou very much for the help. 

I tried this:

tan(2*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2))/tan(2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*10^(-6)*(1/2)) = -4*x^2*(5.555*10^11/(1-.5)^1.2-x^2)^(1/2)*(1.1575*10^12/(1-.5)^1.2-x^2)^(1/2)/(1.1575*10^12/(1-.5)^1.2-2*x^2)^2;

lhs(%)-rhs(%);

RootOf(%, x);

z0 := allvalues(%);

evalf(%);

i get 6 solutions but they seem incorrect:

-1.127205209*10^6, -1.129691937*10^6, -9.942135523*10^5, -1.630716619*10^6, -1.630716619*10^6, 1.129691937*10^6

one of the solutions should be 1.131417176*10^6 (i know this is definately a solution)