document.write( "Question 172148: the product of two consecutive integers is 41 more than their sum. Find the integers. \n" ); document.write( "

Algebra.Com's Answer #132237 by EMStelley(208) $\"\"$ $\"About$

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Call the first integer x. Then the next one can be represented by x+1. Then the product of the two is x(x+1) and \"41 more than their sum\" can be represented by 41+x+x+1. So
\n" ); document.write( " $\"x%28x%2B1%29=41%2Bx%2Bx%2B1\"$
\n" ); document.write( " $\"x%5E2%2Bx=42%2B2x\"$
\n" ); document.write( " $\"x%5E2-x-42=0\"$
\n" ); document.write( " $\"%28x-7%29%28x%2B6%29=0\"$
\n" ); document.write( "So x=7 and x=-6. Which one could be correct? Or both? Let's check. If x=7, the other integer is 8, so
\n" ); document.write( "7(8)=41+7+8
\n" ); document.write( "56=65
\n" ); document.write( "And if x=-6 the other integer is -5, so
\n" ); document.write( "-6(-5)=41+(-6)+(-5)
\n" ); document.write( "30=30
\n" ); document.write( "So both are solutions. \n" ); document.write( "

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