Question 110013
Let x=the smaller integer

Then let x+2=the next integer


IF the sum of the squares of two consecutive positive even integers is 340, then:

{{{x^2+(x+2)^2=340}}}
{{{x^2+(x(x+2)+2(x+2))=340}}}
{{{x^2+((x^2+2x)+(2x+4))=340}}}
{{{x^2+(x^2+(2x+2x)+4)=340}}}
{{{x^2+(x^2+4x+4)=340}}}
{{{(x^2+x^2)+4x+4=340}}}
{{{2x^2+4x+4=340}}}
{{{x^2+2x+2=170}}}
{{{x^2+2x+2-170=170-170}}}
{{{x^2+2x-168=0}}}


BY the quadratic formula,

{{{x=(-2+-sqrt(2^2+4*1*168))/(2*1)}}}
{{{x=(-2+-sqrt(4+672))/(2)}}}
{{{x=(-2+-sqrt(676))/(2)}}}
{{{x=(-2+-26)/(2)}}}
{{{x=(-2+26)/2}}} or {{{x=(-2-26)/(2)}}}
{{{x=24/2=12}}} or {{{x=-28/2=-14}}}

If x=12, x+2=14

If x=-14, x+2=-12


Thus, the numbers maybe (12, 14) or (-14,-12)\


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HyperBrain!