Question

prove that if x and y are odd positive integers, then x square +y square is even but not divisible by 4

Answer 1

hope this help..........

Answer 2

Answer:-

Thinking Process:-

Here, we have to take any two consicutive or positive integer.

After that squaring and adding both the number and check it is a even but not divisible by 4.

Solution:-

Let x = 2m + 1

Let y = 2m + 3

Here, both are positive integer, for  every positive integer m.

⇒ x² + y² = (2m  +1)² + (2m + 3)²

⇒ x² + y² = 4m² + 1 + 4m + 4m² + 9 + 12m      [∵ (a + b)² = a² + 2ab + b²]    

               

⇒ x² + y² = 8m² + 16m² + 10 = even

⇒ x² + y² = 2(4m² + 8m + 5) or (2m² + 4m + 2)

Hence, x² + y² is even for every positive integer m but not divisible by 4.