Question

The three consecutive natural numbers are such that the square of the largest number is greater than the product of the other two by 25 then the largest number is 

1. 8
2. 7
3. 11
4. 9

Answer 1

Correct Answer - Option 4 : 9

Formula used:

(a + b)² = a² + b² + 2ab

Concept used:

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

For example: 1, 2, 3, 4, 5, and so on

Calculation:

Let the three consecutive numbers be x, x + 1, and x + 2

Now, A/Q

⇒ (x + 2)² – x(x + 1) = 25

⇒ x² + 4 + 4x – x² – x = 25

⇒ 3x + 4 = 25

⇒ 3x = 21

⇒ x = 7

∴ The largest number is 9