document.write( "Question 1045089: Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number. \n" ); document.write( "

Algebra.Com's Answer #660590 by KMST(5328) $\"\"$ $\"About$

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Let $\"n-1\"$ , $\"n\"$ , and $\"n%2B1\"$ be the 3 consecutive numbers.
\n" ); document.write( " $\"%28n-1%29n\"$ = the product of the smaller two numbers
\n" ); document.write( " $\"%28n%2B1%29%5E2\"$ = the square of the largest number
\n" ); document.write( " $\"%28n%2B1%29%5E2-19\"$ = 19 less than the square of the largest number
\n" ); document.write( "The problem says that
\n" ); document.write( " $\"%28n-1%29n=%28n%2B1%29%5E2-19\"$ .
\n" ); document.write( "
\n" ); document.write( "Solving that equation:
\n" ); document.write( " $\"%28n-1%29n=%28n%2B1%29%5E2-19\"$
\n" ); document.write( " $\"n%5E2-n=n%5E2%2B2n%2B1-19\"$
\n" ); document.write( " $\"-n=2n-18\"$
\n" ); document.write( " $\"-n%2Bn=2n-18%2Bn\"$
\n" ); document.write( " $\"0=3n-18\"$
\n" ); document.write( " $\"18=3n\"$
\n" ); document.write( " $\"18%2F3=n\"$
\n" ); document.write( " $\"n=6\"$
\n" ); document.write( "The 3 consecutive numbers are
\n" ); document.write( " $\"n-1=6-1=highlight%285%29\"$ , $\"n=highlight%286%29\"$ , and $\"n%2B1=6%2B1=highlight%287%29\"$ .
\n" ); document.write( "
\n" ); document.write( "Verification:
\n" ); document.write( "The product of the smaller two numbers is $\"5%2A6=30\"$
\n" ); document.write( "19 less than the square of the largest number is
\n" ); document.write( " $\"7%5E2-19=49-19=30\"$ \n" ); document.write( "

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