Question 91743
Find two positive consecutive integers such that the sum of their squares = 85.
Let x be the first integer, then x+1 would be the next consecutive integer, so you can write:
{{{x^2 + (x+1)^2 = 85}}} Simplify.
{{{x^2+x^2+2x+1 = 85}}} Subtract 85 from both sides and combine like-terms.
{{{2x^2+2x-84 = 0}}} Solve this quadratic equation by factoring.
{{{(2x-12)(x+7) = 0}}} Apply the zero products principle.
{{{2x-12 = 0}}} or {{{x+7 = 0}}} so...
{{{2x = 12}}}
{{{x = 6}}} or
{{{x+7 = 0}}} so...
{{{x = -7}}} Discard this solution as you are looking for positive values of x.
The two integers are: 6 and 7

{{{6^2+7^2 = 36+49}}} = 85