SOLUTION: Two consecutive integers are added. The square of their sum is 361. What are the integers?

Question 1872: Two consecutive integers are added. The square of their sum is 361. What are the integers?
Found 2 solutions by longjonsilver, Ne0:
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
let the first interger be x and the second be y
we know 2 things...y-x=1 and
sub the first equation, for y, in the second, to give . This becomes
Hence, taking a square root of both sides gives (2x+1) = +19 or -19
Therefore, 2x = 18 or -20 and then x=9 or -10.
Therefore the 2 integers are either (9 and 10) or (-9 and -10)
cheers
Jon.
Answer by Ne0(6) (Show Source): You can put this solution on YOUR website!
The first step in solving problems like this is that you need to define the unknowns that is define what it is your solving for.
We start by letting the first integer be x.
Since the integers are consecutive that means they come one after the other so you can let the second integer be x+1.
The square of their sum is simply adding the two terms together then squaring them like so: . Adding the like terms give us: .
It says the square of their sums is equal to 361 so you now have .
The next step is to solve for x. We can accomplish this by first taking the square roots of both sides like so: . After taking the square root we should arrive with . I had to stick the zero in because the equation editor would not agree with me otherwise. We get x by itself by subtracting 1 then dividing both sides by 2 to get .
Simplifying we get x=9 and x=-10.
By back substituting our value of x into x+1 we get x+1=10 and x+1=-9.
We now have all the integers which are 9,-10,10,-9.
I hope this helps you in solving for problems of this type.
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