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The square of the sum of three consecutive numbers is 225. What are the numbers.

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carolinesmiths | Student, Kindergarten | (Level 1) Salutatorian

Posted September 30, 2013 at 2:15 PM via web

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The square of the sum of three consecutive numbers is 225. What are the numbers.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 30, 2013 at 2:18 PM (Answer #1)

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The square of the sum of three consecutive numbers is 225. Let the numbers be x, x + 1 and x + 2. The sum of the numbers is x +x + 1 + x + 2 = 3x + 3

The square of the sum is (3x + 3)^2 = 225

=> `3x + 3 = sqrt 225`

=> `3x + 3 = +- 15`

=> `x + 1 = +-5`

=> x = 4 and x = -6

The three numbers are either {4, 5, 6} or {-6, -5, -4}

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