Question

The sum of the squares of two natural consecutive
Odd numbers is 394.
The sum of the number is

Answer 1

$\textbf {Hey there, here is the solution.}$

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STEP 1: Define the number:

Let one number be x

The other number is x + 2

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STEP 2: Form the equation:

x² + (x + 2)² = 394

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STEP 3: Solve x:

x² + x² + 4x + 4 = 394

2x² + 4x - 390 = 0

x²+ 2x - 195 = 0

(x - 13)(x + 15) = 0

x = 13 or x = - 15 (rejected, not natural number)

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STEP 4: Find the numbers:

one number = x = 13

The other number = x + 2 = 13 + 2 = 15

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STEP 5: Find the sum of the two numbers:

13 + 15 = 28

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Answer: The sum of the 2 number is 28.

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⭐$\textbf {Cheers}$⭐

Answer 2

Answer:

Let the numbers be x and (x + 2)

• According to the Question :

⇒ x² + (x + 2)² = 394

⇒ x² + x² + 4x + 4 = 394

⇒ 2x² + 4x - 390 = 0

⇒ x² + 2x - 195 = 0

⇒ x² + 15x - 13x - 195 = 0

⇒ (x + 15)(x - 13) = 0

⇒ x = 13

◗ Required sum = 13 + 15 = 28