Question

The sum of the squares of two consecutive odd number is 394. find the numbers.

Answer 1

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Let one of the number be x then the other number be x + 2.

Then according to 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(x+15)−13(x+15)=0⇒(x−13)(x+15)=0⇒x−13=0 or x+15=0⇒x=13 or x=−15

Since, x being an odd number,

Therefore, x = 13.

Then another number will be

x+2=13+2=15

Thus, the two consecutive odd numbers are 13 and 15.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the consecutive odd number be x and x + 2.

According to the Question,

⇒ x² + (x + 2)² = 394

⇒ x² + x² + 4 + 4x = 394

 ⇒ 2x² + 4x + 4 - 394 = 0

⇒ 2x² + 4x - 390 = 0

⇒ x² + 2x - 195 = 0

⇒ x² + 15x - 13x - 195 = 0

 ⇒ x(x + 15) - 13(x + 15) = 0

 ⇒ (x - 13)(x + 15) = 0

⇒ x = 13, - 15  (As x can't be negative)

⇒ x = 13

1st number = x = 13

2nd Number = x + 2 = 13 + 2 = 15

Hence, the two required numbers are 13 and 15.