SOLUTION: The difference between two positive integers is 6. If the smaller is added to the square of the larger, the sum is 266. Find the integers.

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Question 1179497: The difference between two positive integers is 6. If the smaller is added to the square of the larger, the sum is 266. Find the integers.

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
n and n+6;
n%2B%28n%2B6%29%5E2=266
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.
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10 and 16

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Mentally, in a few seconds....

Most of the total of 266 is the square of the larger of the two integers; the largest perfect square less than 266 is 16^2=256; 16-6=10, and 256+10=266.

Answer: 16 and 10.

Algebraically:

Let the two integers be x and x+6. Then

%28x%2B6%29%5E2%2Bx=266
x%5E2%2B12x%2B36%2Bx=266
x%5E2%2B13x-230=0
%28x%2B23%29%28x-10%29=0

x is either -23 or 10; but the problem specified positive integers. So

ANSWERS:
x=10
x+6=16