Given the following statement, compare and contrast how to prove that the statement is true using direct reasoning and how to prove that it is true using indirect reasoning. if x2 = 49, then x = 7 or x = –7.

For the direct proof you must start with the definition original proposition and use the mathematical steps to derive the result.

Original statement: x^2  = 49

Definition if a^2 = b, then a = +√b or a = - √b.

So, x = √49 = 7; or x = -√49 = - 7.

Which prooves directly that x = 7 or x = -7.

The indirect proof is starting from the solution.

If x = - 7, then x^2 = (-7)^2 = 49.

If x = 7, then x^2 = 7^2 = 49.

That is it. You have both the direct proof (from the definition) and the indierect proof.