angel0741 angel0741

20-04-2024
Mathematics

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question eleven
prove that the sum of numbers of the squares of any two consecutive numbers or integers is always an odd number.

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georgepahno georgepahno

20-04-2024

Answer:

Let x be an integer.

x² + (x + 1)² = x² + x² + 2x + 1

= 2x² + 2x + 1

= 2x(x + 1) + 1

2x(x + 1) is always an even integer, so 2x(x + 1) + 1 is always an odd integer.

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