Question

The sum of the squares of two consecutive natural numbers is 25. Represent this situation in the form of a quadratic equation. 

A) x² + (x + 1)² + 25 = 0 

B) x² – (x + 1)² = 25 

C) x² + (x + 1)² = 25 

D) (x + 1)² – x² = 25

Answer 1

Correct option is (C) x² + (x + 1)² = 25

Since, difference between two consecutive natural numbers is 1.

Let x & (x+1) be two consecutive natural numbers.

\(\therefore\) Sum of squares of consecutive natural numbers is \(x^2+(x+1)^2.\)

Given that the sum of the squares of two consecutive natural numbers is 25.

\(\therefore\) \(x^2+(x+1)^2=25\) which represent the given situation.

Answer 2

Correct option is C) x² + (x + 1)² = 25