# The sum of the square of three consecutive numbers is 110. What are the numbers.

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justaguide | Certified Educator

The sum of the square of three consecutive numbers is 110. Let the numbers be x, x+1 and x+2

x^2 + (x + 1)^2 + (x + 2)^2 = 110

=> x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 110

=> 3x^2 + 6x = 105

=> 3x^2 + 6x - 105 = 0

=> 3x^2 - 15x + 21x - 105 = 0

=> 3x(x - 5) + 21(x - 5) = 0

=> (3x + 21)(x - 5) = 0

=> x = -7 and x = 5

**The three numbers are {5, 6, 7} or {-5, -6. -7}**