<PRE><B>Question 451604</B>
Two consecutive numbers are x and x+1 so if their sum is 113 it is


{{{x^2 + (x+1)^2 = 113}}}
{{{x^2 + x^2 + 2x + 1 = 113}}}
{{{2x^2 + 2x - 112 =0}}}

Solutions for x in this quadratic equation are given as


{{{x = (-2 +- sqrt( 2^2-4*2*(-112) ))/(2*2) }}}


It gives us x = 7 or x = -8

So numbers are 7 and 8, or -8 and -7.


Check1:  {{{7^2+8^2= 49 + 64 = 113}}}, OK
Check2: {{{(-8)^2 + (-7)^2 = 64 + 49 = 113}}}, OK

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