SOLUTION: Find two consecutive positive integers such that the sum of their square is 85. I think I start with square root of x plus the square root of x + 1 = 85. If so then I don

Question 45380: Find two consecutive positive integers such that the sum of their square is 85.
I think I start with square root of x plus the square root of x + 1 = 85.
If so then I don't know where to go from here.
Thanks for help.
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Not quite...the setup is like this
x^2 + (x + 1)^2 = 85
(the sum of the squares)
Now we get
x^2 + x^2 + 2x + 1 = 85
2x^2 + 2x - 84 = 0
x^2 + x - 42 = 0
(x + 7)(x - 6) = 0
and
x = -7 or x = 6
but they must be positive, hence your numbers are
6 and 7
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