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.

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) (Show Source): You can put this solution on YOUR website!
n and n+6;

.
.
.
10 and 16
Answer by greenestamps(13203) (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

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

ANSWERS:
x=10
x+6=16

RELATED QUESTIONS
The difference between two positive integers is 6. If the smaller is added to the square (answered by josgarithmetic)
The difference between two positive integers is 5. If the smaller is added to the square... (answered by stanbon)
The difference between two positive integers is 4. If the smaller is added to the square... (answered by mananth)
The difference between two positive integers is 5. If the smaller number is added to the... (answered by oscargut)
The difference between two positive integers is 3. If the smaller is added to the square... (answered by josh_jordan,MathTherapy)
The difference between two positive intergers is 8. If the smaller is added to the square (answered by robertb)
The difference between two positive integers is 4. If the smaller is added to the square... (answered by josgarithmetic)
the difference between two positive integers is 3. If the smaller is added to the square... (answered by jpvn2015)
two positive integers with a difference of six. if the smaller is added to the square of... (answered by moshiz08)