Two numbers differ by 12. If their product is increased by the square of their difference, the result is 1008. Find the larger number.
Show answer & explanation
Correct answer: D
Explanation
Given:
Difference of two numbers = 12
Product + (Square of the difference) = 1008
By the formula:
Square of the difference = 12 × 12
Let the smaller number = x
Larger number = x + 12
Square of the difference = 12 × 12 = 144
Now,
x(x + 12) + 144 = 1008
x² + 12x + 144 = 1008
x² + 12x − 864 = 0
(x + 36)(x − 24) = 0
x = 24
Larger number = x + 12 = 24 + 12 = 36