x = smaller natural number
x+1 = larger natural number
x² + (x+1)² = 113
x² + (x+1)(x+1) = 113
x² + x² + 2x + 1 = 113
2x² + 2x - 112 = 0
x² + x - 56 = 0
(x + 8)(x - 7) = 0
x + 8 = 0 ; x - 7 = 0
x = -8; x = 7
Since we are told the answers are natural numbers,
we know that they are positive integers, so we
discard the -8 and
x = smaller natural number = 7
x+1 = larger natural number = 7+1 = 8
Edwin
You can put this solution on YOUR website! If the first number is x then the next natural number will be x + 1.
The sum of the squares will therefore be
x^2 + (x + 1)^2
x^2 + x^2 + 2x + 1
ie 2x^2 + 2x + 1
This must equal 113 so
2x^2 + 2x + 1 = 113
Subtract 113 from each side of the equation to get
2x^2 + 2x + 1 -113 = 113 - 113
2x^2 + 2x - 112 = 0
Take out a common factor of 2 and divide each side of the equation by 2 to get
x^2 + x - 56 = 0
This factorises to get
(x + 8)(x - 7)= 0
ie x = -8 or 7
The numbers must be natural numbers so that excludes -8.
ie x must be 7 and the other consecutive number must be 8.
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