angel0741
angel0741 angel0741
  • 20-04-2024
  • Mathematics
Answered

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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Answer :

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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