Math, asked by nischalrathor, 1 year ago

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

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Answered by trisha10433
0
hey there this question is answered by another brainly user also hope it helps :)
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Answered by fanbruhh
1

Step-by-step explanation:

we know that any odd positive integer is of the form 2q+1 for some integer q.

so, let x = 2m+1 and y = 2n+1 for some integers m and n.

•°• x²+y²= ( 2m+1)²+(2n+1)²

==> x²+y²=4(m²+n²)+4(m+n)+2

==> x²+y²= 4{(m²+n²)+(m+n)} +2

==> x²+y² = 4q +2 , where q= (m²+n²)+(m+n)

==> x²+y² is even and leaves remainder 2 when divided by 4.

==> x²+y² is even but not divisible by 4.

HENCE PROVED✔✔

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