SOLUTION: one positive integer is 4 more than another. the sum of their squares is 40. Find the numbers.

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Question 79042: one positive integer is 4 more than another. the sum of their squares is 40. Find the numbers.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be a and b.
a = b+4 and
a%5E2%2Bb%5E2+=+40 Substitute the a = b+4 here and solve for b.
%28b%2B4%29%5E2%2Bb%5E2+=+40 Simplify.
%28b%5E2%2B8b%2B16%29%2Bb%5E2+=+40
2b%5E2%2B8b%2B16+=+40 Now subtract 40 from both sides.
2b%5E2%2B8b-24+=+0 Divide through by 2 to simplify.
b%5E2%2B4b-12+=+0 Solve this quadratic equation by factoring.
%28b-2%29%28b%2B6%29+=+0 Apply the zero products principle.
b-2+=+0 or b%2B6+=+0, so..
b+=+2 or b=+-6 Discard the negative solution as you are looking for positive integers only.
a+=+b%2B4
a+=+2%2B4
a+=+6
The two integers are: 2 and 6
Check:
2%5E2+%2B+6%5E2+=+4+%2B+36 = 40
and...
2%2B4+=+6