Question

please help me to solve this question it is very urgent class 10 chapter 1 question no
9

Answer 1

Let the two odd positive numbers be x = 2k + 1 a nd 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 number is not divisible by 4.
Hence if x and y are odd positive integers, then x2 + y2 is even but not divisible by 4
4

Answer 2

Let x = 2p + 1 and y = 2q + 1.

x^2 + y^2:

= > (2p + 1)^2 + (2q + 1)^2

= > 4p^2 + 1 + 4p + 4q^2 + 1 + 4q

= > 4p^2 + 4q^2 + 4p + 4q + 2

= > 2(2p^2 + 2q^2 + 2p + 2q + 1)


This proves that the expression is divisible by 2 but not by 4.

Therefore x^2 + y^2 is even but not divisible 4.



Hope this helps!