If m + n = 14 and mn = 48, then fi nd the value(s)of m − n.

To find the value(s) of m - n, we can use the given equations:

1. m + n = 14
2. mn = 48

Step 1: Solve equation 1 for m or n. Let's solve equation 1 for m: m = 14 - n

Step 2: Substitute the value of m from step 1 into equation 2. (14 - n)n = 48

Step 3: Simplify the equation. 14n - n^2 = 48

Step 4: Rearrange the equation to a quadratic form. n^2 - 14n + 48 = 0

Step 5: Factorize the quadratic equation. (n - 6)(n - 8) = 0

Step 6: Set each factor equal to zero and solve for n. n - 6 = 0 or n - 8 = 0 n = 6 or n = 8

Step 7: Substitute the values of n into equation 1 to find the corresponding values of m. For n = 6: m + 6 = 14 m = 14 - 6 m = 8

For n = 8: m + 8 = 14 m = 14 - 8 m = 6

Step 8: Calculate the value of m - n for each solution. For n = 6: m - n = 8 - 6 m - n = 2

For n = 8: m - n = 6 - 8 m - n = -2

Therefore, the values of m - n are 2 and -2.