Question 65708
Find two consecutive positive intergers such that the sum of their square is 85

Let the first integer be: x
Then the next consecutive integer is: x+1
Sum means add.
Square means raise to the second power
is means =.
{{{x^2+(x+1)^2=85}}}
{{{x^2+x^2+2x+1=85}}}
{{{2x^2+2x+1=85}}}
{{{2x^2+2x+1-85=85-85}}}
{{{2x^2+2x-84=0}}}
{{{2(x^2+x-42)=0}}}
{{{2(x^2+x-42)/2=0/2}}}
{{{x^2+x-42=0}}}
(x+7)(x-6)=0
x+7=0 or x-6=0
x+7-7=0-7 or x-6+6=0+6
x=-7 or x=6
Since you were asked for two consecutive POSITIVE integers
The first integer is: x=6
and the second is: x+1=6+1=7
:
Sanity check:
are 6 and 7 consecutive integers? Yes!
Do the sum of their squares=85?
6^2+7^2=85
36+49=85
85=85 Yes!
It appears that we're sane...for now.
Happy Calculating!!!