Question 1062166


Let x be the smaller number
    x+2 = next number
    x+4 = final number

{{{ x^2 + (x+2)^2 = (x+4)^2 + 9 }}}
{{{ x^2 + (x^2+4x+4) = (x^2+8x+16) + 9 }}}
{{{   2x^2 + 4x + 4 = x^2 + 8x + 25 }}}
{{{   x^2 - 4x - 21 = 0 }}}
{{{ (x-7)(x+3) = 0 }}}
{{{ x=7 }}} and/or {{{ x=-3 }}}
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Check if either or both x values work:
   #1  -3, -1, 1
          {{{ (-3)^2 + (-1)^2 = 9+1  = 10 }}}
         {{{ (1)^2 + 9 = 10 }}}  (ok)

   #2  7, 9, 11
          {{{ 7^2 + 9^2 = 49+81 = 130 }}}
          {{{ 11^2 + 9 = 121+9  = 130 }}}  (ok)

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Answer:
Although both answers work, I just noticed it asked for positive numbers only, so just this one answer is valid:
      7, 9, 11