SOLUTION: The sum of the squares of two consecutive even integers is 100. Find the integers

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The sum of the squares of two consecutive even integers is 100. Find the integers       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 258037: The sum of the squares of two consecutive even integers is 100. Find the integers
Found 2 solutions by drk, unlockmath:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Let X and (X+2) be the consecutive even integers. We get
(i) x%5E2+%2B+%28x%2B2%29%5E2+=+100
expanding, we get
(ii) x%5E2+%2B+x%5E2+%2B+4x+%2B+4+=+100
setting = 0, we get
(iii) 2x%5E2+%2B+4x+-96+=+0
dividing by 2, we get
(iv) x%5E2+%2B+2x+-+48+=+0
factoring, we get
(v) %28x%2B8%29%28x-6%29+=+0
solving for x, we get
x = -8
and x = 6.
so, we have
(-8, -6) OR (6,8)

Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
Let's set up one integer to be x and the other one to be x+2. Now we can set up an equation to be:
x^2+(x+2)^2=100 rewritten as:
x^2+x^2+4x+4=100 Subtract 100 from each side:
x^2+x^2+4x-96=0 Combine like terms:
2x^2+4x-96=0 Factor out 2 to give us:
2(x^2+2x-48)=0 Now we can factor this to be:
2(x+8)(x-6)=0 Solve for x
x=-8
x=6
6 is the only one that works.
So the two integers are 6 & 8
RJ
Check out a new math book I wrote at:
www.math-unlock.com