Prove that x and y both odd poditive integers then x^2+y^2is even but not divisible by 4
Answers
Answered by
9
ANSWER:
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
hope this helps you
Similar questions
Math,
6 months ago
Physics,
6 months ago
Physics,
6 months ago
Science,
11 months ago
Social Sciences,
11 months ago
English,
1 year ago
Social Sciences,
1 year ago