#### Question

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

#### Solution

Let the consecutive odd positive integers are 2x – 1 and 2x + 1

Given that the sum of the squares is 394.

⇒ (2𝑥 - 1)^{2} + (2𝑥 + 1)2 = 394

⇒ 4𝑥^{2} + 1 - 4𝑥 + 4𝑥^{2} + 1 + 4𝑥 = 394

⇒ 8𝑥^{2} + 2 = 394

⇒ 4𝑥^{2} = 392

⇒ 𝑥^{2} = 36

⇒ x = 6

As x = 6, 2x - 1 = 2 × 6 - 1 = 11

2x + 1 = 2 × 6 + 1 = 13

∴ The two consecutive odd positive numbers are 11 and 13.

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#### APPEARS IN

Solution The Sum of the Squares of the Two Consecutive Odd Positive Integers as 394. Find Them. Concept: Solutions of Quadratic Equations by Factorization.