document.write( "Question 177196: find three consecutive integers such that the product of the two smaller inters is 2 more than ten times the largest integers. \n" ); document.write( "

Algebra.Com's Answer #132238 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the three consecutive integers be: x, (x+1) and (x+2)
\n" ); document.write( " $\"x%2A%28x%2B1%29+=+10%28x%2B2%29%2B2\"$ \"The product of the two smaller integers (x and (x+1)) is 2 more than 10 times the larger integer (x+3).
\n" ); document.write( " $\"x%5E2%2Bx+=+10x%2B20%2B2\"$ Subtract 10x from both sides.
\n" ); document.write( " $\"x%5E2-9x+=+22\"$ Subtract 32 from both sides.
\n" ); document.write( " $\"x%5E2-9x-22+=+0\"$ Factor this quadratic equation.
\n" ); document.write( " $\"%28x-11%29%28x%2B2%29+=+0\"$ Apply the zero product rule.
\n" ); document.write( " $\"x-11+=+0\"$ or $\"x%2B2+=+0\"$ so...
\n" ); document.write( " $\"x+=+11\"$ or $\"x+=+-2\"$
\n" ); document.write( "Solutions:
\n" ); document.write( "11, 12, and 13
\n" ); document.write( "-2, -1, and 0
\n" ); document.write( "As you can see, there are two solutions, so let;'s check them both!
\n" ); document.write( "x = 11
\n" ); document.write( " $\"%2811%29%2A%2812%29+=+10%2813%29%2B2\"$
\n" ); document.write( " $\"132+=+130%2B2\"$
\n" ); document.write( " $\"132+=+132\"$ OK!
\n" ); document.write( "x = -2
\n" ); document.write( " $\"%28-2%29%2A%28-1%29+=+10%280%29%2B2\"$
\n" ); document.write( " $\"2+=+2\"$ OK!
\n" ); document.write( " \n" ); document.write( "

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