Find the larger of the two numbers if their difference is 4 and the difference of the squares is 104.

Let the smaller number be x, then the larger number is (x + 4). By the condition of the problem, it is known that the difference between the squares of these numbers is equal to ((x + 4) ^ 2 – x ^ 2) or 104. Let’s compose an equation and solve it.

(x + 4) ^ 2 – x ^ 2 = 104 – open the bracket by the formula (a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2, where a = x, b = 4;

x ^ 2 + 2 * x * 4 + 4 ^ 2 – x ^ 2 = 104;

x ^ 2 + 8x + 16 – x ^ 2 = 104;

8x + 16 = 104;

8x = 104 – 16;

8x = 88;

x = 88: 8;

x = 11 – smaller number;

x + 4 = 11 + 4 = 15 is the larger number.

Answer. The larger number is 15.