SOLUTION: Find two consecutive positive integers such that the sum of their square is 85. Your help will be very appreciated! Thanks so much! ac

You can put this solution on YOUR website!
Let the consecutive integers equal x and x+1


This can be solved either by the quadratic formula
of by completing the square. I'll complete the square
subtract 1 from both sides

divide both sides by 2

to complete the square, take one-half of the coeffecient
of x, square it, and add it to both sides
Half of 1 is 1/2 and (1/2)^2 = 1/4






and



The problem wants 2 consecutive POSITIVE integers, so I'll
pick x = +6

The answers are +6 and +7
check:



OK