Final answer:
The value of m⁴ + 1/m⁴, if m - 1/m = 3, is approximately 84.
Step-by-step explanation:
To find the value of m4 + 1/m4 given m - 1/m = 3, let's first simplify the expression. Multiplying both sides of the equation by m, we get m2 - 1 = 3m. Rearranging the terms, we have m2 - 3m - 1 = 0. Solving this quadratic equation using the quadratic formula, we find that m is approximately equal to 1.381966011250105. Now we can substitute this value into the expression to find:
m4 + 1/m4 = (1.381966011250105)4 + 1/(1.381966011250105)4
Calculating this expression, we find that the value is approximately 84.