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Prove that if x and y are odd positive integers, then x2 +y2 is even but not divisible by 4

Posted by Aarushi Yadav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

3 answers

Aarushi Yadav 6 years, 11 months ago

Thanks

0Thank You

Ram Kushwah 6 years, 11 months ago

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

2Thank You

Ansh Nanesha 6 years, 11 months ago

Shut up re

0Thank You

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CBSE > Class 10 > Mathematics