Let 1 number be `x` . Since the numbers are consecutive, the other number would be `x + 1.`
Square both and add together to equal 313.
`x^2 + (x+1)^2 = 313`
`x^2 + x^2 + 2x + 1 = 313`
`2x^2 + 2x - 312 = 0`
`x^2 + x - 156 = 0`
`(x - 12)(x + 13) = 0`
`x = 12, x = -13`
Since the number are defined to be natural, x = -13 is not a solution.
Therefore, `x = 12` , and `x+1 = 13` .
The two numbers are 12 and 13.
`12^2 + 13^2 = 313`
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