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Prove that if x and y …

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

    • Posted by Rithin Smart 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Prince Raj 6 years, 4 months ago

    Understood

    0Thank You

    Prince Raj 6 years, 4 months ago

    Let the two positive odd integers be x=2m+1 and y=2n+1 where m and n is any positive integet because if a no. is multiplied by 2 it is even no. and then added by 1 then it changes to odd. ATQ x²+y²=(2m+1)²+(2n+1)² =4m²+1+4m+4n²+1+4n =4m²+4n²+4m+4n+2 =4(m²+n²+m+n)+2 Since the sum of square of any positive odd integar is always even And the unit digit of no. is 2 which is not fulfilled the divisibility rule of 4(the sum of the digits of the no.is divisible by 4 then the original no. is also perfectly divisible by 4Hence the square of x+y is even but not divisible by 4

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