1.

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

Answer»

Given:-

  • x and y are ODD positive integers.

To Prove:-

  • x² + y² is even but not divisible by 4.

step-by-step SOLUTION:-

Let the two odd NUMBERS be (2a+1) & (2b+1) because if we add 1 to any even no. it will be odd.

x²+y²

  • → (2a + 1)² + (2b + 1)²
  • → (4a² + 4a + 1) + (4b²+ 4b + 1)
  • → 4(a² + b² + a + b)+2

4 Is not a multiple of 2 it means CLEARLY that 4 is not multiple of x²+y² , so x²+y² is even but not divisible by 4.

Hence proved.!!


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