Final answer:
By substituting the expressions X = (a + 7) and Y = (a - 7) into the equation and applying the difference of squares formula, it is shown that a^2 equals xy + 49.
Step-by-step explanation:
To show that a2 = xy + 49 where X = (a + 7) and Y = (a - 7), we will use the given equations to find the product of x and y.
Firstly, substitute the expressions for x and y into the equation xy:
xy = (a + 7)(a - 7)
Now, apply the difference of squares formula, which is (p + q)(p - q) = p2 - q2:
xy = a2 - 72
Calculate 72:
xy = a2 - 49
Add 49 to both sides of the equation to get:
a2 = xy + 49
Thus, we have proven that a2 equals to the product of x and y plus 49.