Question

9. Prove that if x and y are both odd positive integers then x^2 +y^2 is even
but not divisible by 4​

Answer 1

Answer:

let x=1 and y=1 be the two odd positive integers

so,x^2+y^2=1^2+1^2

=》2

which is even but not divisible by 4

hance proved

Answer 2

Answer:Let the two odd positive no. be x = 2k + 1 and y = 2p + 1

Hence, x2 + y2 = (2k + 1)2 +(2p + 1)2

= 4k2 + 4k + 1 + 4p2 + 4p + 1

= 4k2 + 4p2 + 4k + 4p + 2

= 4 (k2 + p2 + k + p) + 2

clearly, notice that the sum of square is even the no. is not divisible by 4

hence, if x and y are odd positive integer, then x2 + y2 is even but not divisible by four.