Question 74285
Find two consecutive positive integers such that the sum of their squares is 85.
:
Let the 1st number be: x
Then the next consecutive number is: x+1
sum means: +
Squares means: ^2
is means: =
{{{x^2+(x+1)^2=85}}}
{{{x^2+(x+1)(x+1)=85}}}
{{{x^2+x(x+1)+1(x+1)=85}}}
{{{x^2+x(x)+x(1)+1(x)+1(1)=85}}}
{{{x^2+x^2+x+x+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
We are only interested in positive integers, so throw out the -7.
The first integer is: x=6
The second integer is: x+1=6+1=7
:
Sanity Check:
If you added their squares would you get 85?
{{{6^2+7^2=85}}}
{{{36+49=85}}}
{{{85=85}}}
We seem to be on the right track.
Happy Calculating!!!!