SOLUTION: The sum of the squares of two consecutive positive odd integers is 130. Find the two integers

Question 271017: The sum of the squares of two consecutive positive odd integers is 130. Find the two integers
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
x = first positive odd integer
y = second positive odd integer
y = x+2 = the second positive odd integer is consecutive to x.
.
x +y = 130
substituting
x + x+2 = 130
2x + 2 = 130
subtracting 2 from both sides
2x = 128
dividing both sides by 2
x = 64, and it is NOT ODD !
So, there is no solution with odd integers.
.
To check, we can explore the relationship of "nearby" odd integers:
x = 65
y = x+2 = 67
x+y = 132
.
x = 63
y = x+2 = 65
x+y = 128
.
So there is no solution with consecutive odd numbers.
.
If the original problem were to have been x+y = 132, then the solution would have been 65 and 67.
But that was not what was given.
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