The sum of the squares of two consecutive odd natural numbers is 74. The greater number is :

1. 5

2. 7

3. 9

4. none of these

Let the two consecutive odd natural numbers be x and x + 2.

Given,

Sum of the squares of two consecutive odd natural numbers is 74.

⇒ x² + (x + 2)² = 74

⇒ x² + x² + 4 + 4x = 74

⇒ 2x² + 4x + 4 - 74 = 0

⇒ 2x² + 4x - 70 = 0

⇒ 2x² + 14x - 10x - 70 = 0

⇒ 2x(x + 7) - 10(x + 7) = 0

⇒ (2x - 10)(x + 7) = 0

⇒ (2x - 10) = 0 or (x + 7) = 0     [Using zero-product rule]

⇒ 2x = 10 or x = -7

⇒ x = $\dfrac{10}{2}$ or x = -7

⇒ x = 5 or x = -7

Since the number required is natural number, thus x ≠-7.

x + 2 = 5 + 2 = 7.

The greater number among the two numbers is 7.

Hence, option 2 is the correct option.