document.write( "Question 866162: the difference between 2 positive integers is 5. if the smaller is added to the square of the larger,the sum is 301, find the integers.
\n" ); document.write( "please help me and i thank you in advance. \n" ); document.write( "
Algebra.Com's Answer #522086 by DrBeeee(684)\"\" \"About 
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Let a = the smaller positive integer and
\n" ); document.write( "let b = the larger positive integer
\n" ); document.write( "Then we have two equations
\n" ); document.write( "(1) b - a = 5 and
\n" ); document.write( "(2) a + b^2 = 301
\n" ); document.write( "Solve (1) for b and substitute it into (2) and get
\n" ); document.write( "(3) a + (5 + a)^2 = 301 or
\n" ); document.write( "(4) a + 25 + 10a +a^2 - 301 = 0 or
\n" ); document.write( "(5) a^2 + 11a - 276 = 0
\n" ); document.write( "Use the quadratic equation solution formul
\n" ); document.write( "(6) \"%28-11%2B-sqrt%2811%5E2-4%2A1%2A%28-276%29%29%2F%282%2A1%29%29\" and get
\n" ); document.write( "(7) a = {-23,12}
\n" ); document.write( "We select a = 12, because it must be a positive integer. Using (1) we get
\n" ); document.write( "(8) b = 5 + 12 or
\n" ); document.write( "(9) b = 17
\n" ); document.write( "Check these values using (2).
\n" ); document.write( "Is (12 + 17^2 = 301)?
\n" ); document.write( "Is (12 + 289 = 301)?
\n" ); document.write( "Is (301 = 301)? Yes
\n" ); document.write( "Answer: The two positive integers are 12 and 17.
\n" ); document.write( "PS a = -23 and b = -18 should also be a solution. Try it in (2). \n" ); document.write( "
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