Question

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

Answer 1

Answer:

Step-by-step explanation:

Let the two consecutive +ve odd numbers be x , x+2

given.

x² + (x+2)² = 394

x² + x² + 4x + 4 = 394

2x² +4x - 390 = 0

x² + 2x - 195 = 0

 (x - 13 ) ( x + 15 )  = 0

x = 13 , x = - 15

since the odd no, is +ve ,  x = 13

∴ the numbers are 13 and 15

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 Numbers :

◗ x = 13

◗ (x + 2) = 13 + 2 = 15