Final answer:
To solve the equation x^3 - 6x = 72 between 4 and 5, the two appropriate methods are trial and error or graphing; factoring or substitution methods are not suitable in this context.
Step-by-step explanation:
To find the solution to the equation x^3 - 6x = 72 between 4 and 5, multiple methods can be used, but the most appropriate methods considering the interval provided would be either trial and error or graphing.
Factoring could be attempted, but the equation doesn't factor nicely, and the substitution method isn't relevant here since we are dealing with a single equation with a single unknown.
By graphing the function f(x) = x^3 - 6x - 72, one can visually estimate the root between 4 and 5. Alternatively, trial and error involve plugging in values within the interval until the left-hand side of the equation closely approximates the right-hand side. Given these approaches, both trial and error or graphing are acceptable answers.