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

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

Maple

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. Regards,

Erik V.

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