Question 1179497
<br>
Mentally, in a few seconds....<br>
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.<br>
Answer: 16 and 10.<br>
Algebraically:<br>
Let the two integers be x and x+6. Then<br>
{{{(x+6)^2+x=266}}}
{{{x^2+12x+36+x=266}}}
{{{x^2+13x-230=0}}}
{{{(x+23)(x-10)=0}}}<br>
x is either -23 or 10; but the problem specified positive integers.  So<br>
ANSWERS:
x=10
x+6=16<br>