Given information:
We are given that α and β are the roots of the equation x^2 + 7x + 12 = 0.

To find:
We need to find the equation whose roots are (α + β)^2 and (α - β)^2.

Solution:

Step 1: Find the sum and product of the roots
The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by the formula:
Sum of roots = -b/a

In this case, the sum of the roots α and β is -7/1 = -7.

The product of the roots of a quadratic equation ax^2 + bx + c = 0 is given by the formula:
Product of roots = c/a

In this case, the product of the roots α and β is 12/1 = 12.

Step 2: Find the value of (α + β)^2 and (α - β)^2
We know that (α + β)^2 = (sum of roots)^2 = (-7)^2 = 49

We also know that (α - β)^2 = (sum of roots)^2 - 4(product of roots) = 49 - 4(12) = 49 - 48 = 1

Therefore, (α + β)^2 = 49 and (α - β)^2 = 1.

Step 3: Write the equation with roots (α + β)^2 and (α - β)^2
Let the equation with roots (α + β)^2 and (α - β)^2 be x^2 + mx + n = 0.

We know that the sum of the roots is equal to the opposite of the coefficient of x divided by the coefficient of x^2. Therefore, the sum of the roots is -m/1 = -m.

From step 2, we know that the sum of the roots (α + β)^2 and (α - β)^2 is 49 and 1 respectively.

Equating the sum of the roots to -m, we have -m = 49 and -m = 1.

Therefore, m = -49 and m = -1.

Step 4: Write the equation with roots (α + β)^2 and (α - β)^2
Substituting the value of m in the equation x^2 + mx + n = 0, we have:

For (α + β)^2:
x^2 - 49x + n = 0

For (α - β)^2:
x^2 - x + n = 0

Conclusion:
The equation whose roots are (α + β)^2 and (α - β)^2 is:
For (α + β)^2:
x^2 - 49x + n = 0

For (α - β)^2:
x^2 - x + n = 0