Question 212038
Let x = the first positive integer, the x+1 = the next consecutive positive integer. The sum of the squares of these is 85.
{{{x^2+(x+1)^2 = 85}}} Simplify.
{{{x^2+(x^2+2x+1) = 85}}} 
{{{2x^2+2x +1 = 85}}} Subtract 1 from both sides.
{{{2x^2+2x = 84}}} Divide both sides by 2.
{{{x^2+x = 42}}} Subtract 42 from both sides.
{{{x^2+x-42 = 0}}} Factor the trinomial.
{{{(x+7)(x-6) = 0}}}
{{{(x+7) = 0}}} or {{{(x-6) = 0}}} so...
{{{x = -7}}} or {{{x = 6}}} Ignore the negative solution.
{{{x = 6}}}
The two integers are: 6 and 7