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Proue that if x andy are odd positive in tegenthen &? ty? is even but not divisible by 4. |
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Answer» Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1Hence x^2+ y^2= (2k + 1)^2+ (2p + 1)2 = 4k^2+ 4k + 1 + 4p2+ 4p + 1 = 4k^2+ 4p2+ 4k + 4p + 2 = 4(k^2+ p^2+ k + p) + 2Clearly notice that the sum of square is even the number is not divisible by 4Hence ifx andy areodd positive integers, then x^2+ y^2is even but not divisible by 4 |
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