The product of two consecutive even numbers is 1088. What is the difference of the larger number and the square of the smaller number?

Correct option is D

Given:

Let the two consecutive even numbers be x and x + 2.

The product of these numbers is given as 1088.

Solution:

The equation representing the product of two consecutive even numbers:

x(x + 2) = 1088

​$$x^2 + 2x = 1088$$​​

​$$x^2 + 2x - 1088 = 0$$

$$x^2 + 34x - 32x - 1088 = 0$$​​​

x(x + 34) - 32(x + 34) = 0

(x - 32)(x + 34) = 0

x = 32 , x = -34

Since x represents an even number, we take x = 32.

The larger number:

x + 2 = 32 + 2 = 34

Calculating the difference between the larger number and the square of the smaller number:

​$$32^2 - 34 = 1024 - 34 = 990$$​​

Thus, the correct option is (d) ₹990