The sum of the squares of two consecutive odd positive integers is 394. Find them.

Given: Let a, a+2 be two consecutive odd numbers.

a² + (a + 2)² = 394

To find: The value of a, a+2

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x² and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

the consecutive odd integers be a, a + 2

According to question,

a² + (a + 2)² = 394

Split the middle terms.

⇒ a² + a² + 4a + 4 = 394

⇒ a² + 2a – 195 = 0

⇒ a² + 15a – 13a – 195 = 0

⇒ a (a + 15) – 13(a + 15) = 0

⇒ (a – 13) (a + 15) = 0

⇒ a = 13, -15

The numbers are 13 and 15.