Question: Seeking a good praxis in solving equations in High School and College

Dear Maple users

Many problems in mathematicis can be traced back to solving equations. It is at the heart of a program like Maple. I know solving equations in general can be immensely difficult. As an example The Riemann hypothesis has to do with the solution of a specific equation, the Riemann zeta function, and is probably the most famous unsolved problem today. I just mention this one to emphasize how hard it can be to solve an equation. Therefore I know we cannot expect too much of a program like Maple. It handles families of equations perfectly well, for example polynomials. When dealing with for example transcendental equations - even simple-looking ones like the one below - it is another matter (numerical solutions).

What I am asking for here is a discussion about a best praxis in dealing with equations in High School and College. Those people don't get the most nasty equations, and I am only asking for equations of one variable. Also I am mainly interested in only numerical reel solutions. What would you tell a student to do when solving equations? Obviously the instructions should not be too involved and should lead to all solutions ... or at least to all solutions with a very high probability, when there are finite many.

To start the discussion I have tried solving a transcendental equation using four different methods and none of them succeed in delivering all four solutions in one step.

Method 1: Using the solve command
Method 2: Using the solve command with the decimal-point-trick (One of numbers in the equation is written with a decimal point to force Maple to "think" in numeric terms)
Method 3: Using the fsolve command
Method 4: Using the Roots command in a student package.


Erik V.

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