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  • 24-07-2022
  • Mathematics
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Prove: The square of a number that is two more than a multiple of 3 is one more than a multiple of 3.

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reinhard10158
reinhard10158 reinhard10158
  • 05-08-2022

Step-by-step explanation:

x is the number

x = 3y + 2

the square

x² = (3y + 2)² = 9y² + 12y + 4

9y² is a multiple of 3 (because of the factor 9)

12y is a multiple of 3 (because of the factor 12)

4 is 1 more than a multiple of 3 (1×3).

so, the sum of all 3 terms is 1 more than a multiple of 3.

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