Question

The product of two consecutive even whole numbers is 24, the numbers are ______.

विकल्प

• – 8 and – 2

• 3 and 8

• – 4 and – 6

• 4 and 6

Answer 1

The product of two consecutive even whole numbers is 24, the numbers are 4 and 6.

Explanation:

Given consecutive even whole numbers are 2x and 2(x + 1)

Then, according to given condition, we have

2x × 2(x + 1) = 24

`\implies` 4x(x + 1) = 24

`\implies` x(x + 1) = `24/4` = 6

`\implies` x² + x – 6 = 0

`\implies` x² + 3x – 2x – 6 = 0

`\implies` x(x + 3) – 2(x + 3) = 0

`\implies` (x + 3)(x – 2) = 0

Either x + 3 = 0 or x – 2 = 0

`\implies` x = – 3 or x = 2

`\implies` x = – 3 or 2

Since x is an whole number

∴ x ≥ 0

∴ x ≠ – 3 thus x = 2

∴ Consecutive even whole numbers are 2 × 2 and 2(2 + 1)

i.e. 4 and 6