document.write( "Question 900033: The difference between the squares of two positive integers is 376 and their positive difference is as small as possible. What is the value of their positive difference? \n" ); document.write( "

Algebra.Com's Answer #545807 by Edwin McCravy(20056) $\"\"$ $\"About$

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Let the two positive integers be p and q, p > q\r\n" );
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document.write( "p² - q² = 376\r\n" );
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document.write( "(p-q)(p+q) = 376\r\n" );
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document.write( "So (p-q) and (p+q) are two integers, (p-q) < (p+q),\r\n" );
document.write( "whose product is 376.  The only pairs of factors\r\n" );
document.write( "with product 376 are\r\n" );
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document.write( "1,376\r\n" );
document.write( "2,188\r\n" );
document.write( "4,94\r\n" );
document.write( "8,47\r\n" );
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document.write( "So we have 4 possible systems of equations:\r\n" );
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document.write( ",,,\r\n" );
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document.write( "The solution to the first system is (p,q) = (188.5,187.5),\r\n" );
document.write( "and those aren't even positive integers.  So the smallest\r\n" );
document.write( "possible positive difference of p and q can't be 1.\r\n" );
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document.write( "The solution to the second system is (p,q) = (95,93), and\r\n" );
document.write( "the positive difference of them is 2.  So that's the answer.\r\n" );
document.write( "We don't need to solve the other two systems, since p and q\r\n" );
document.write( "differ by more than 2 in those.\r\n" );
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document.write( "Answes:  It's the positive difference of 95-93, which is 2.\r\n" );
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document.write( "Edwin

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