Question

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

Answer 1

Answer:

The numbers are 13 and 15

Step-by-step explanation:

Let the numbers be a and a+2

a^2+(a+2)2=394

2a^2+4a+4=394

2a(a+2)=390

a(a+2)=195=13×15

Therefore,

a=13

a+2=15

Answer 2

Two numbers are 13 and 15.

Step-by-step explanation:

Given: The sum of the squares of two consecutive odd positive integers is 394.

Solution:

Let the consecutive odd positive integers be x and x+2.

Given that x² + (x+2)² = 394

x² + x² + 4 + 4x = 394

2x² + 4x - 390 = 0

Dividing by 2, we get: x² + 2x - 195 = 0

x² - 15x - 13x - 195 = 0

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

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

Therefore x = 13, 15.

So the two numbers are 13 and 15.

13² + 15² = 369 + 225 = 394