SOLUTION: The sum of the squares of two positive consecutive odd integers is 394. Find the integer.

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Question 20931: The sum of the squares of two positive consecutive odd integers is 394. Find the integer.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
let any number be x ...then 2x will be always even....if we subtract 1 from it it will be always odd
so 2x-1 is one odd number ..its next odd number will be 2x-1+2=2x+1
so sum of their squares
(2x-1)^2+(2x+1)^2=394
2[(2x)^2+(1)^2]=394...using formula (a+b)^2+(a-b)^2=2[(a)^2+(b)^2]
(4x^2+1)=394/2=197
4x^2=197-1=196
x^2=196/4=49
x=7...hence the 2 numbers are 2*7-1=14-1=13 and 15...you can easily verify
13^2=169
15^2=225
sum is 394