document.write( "Question 155016: What two consecutive integers have cubes that differ by 217? \n" ); document.write( "

Algebra.Com's Answer #114146 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the first integer be x, the next consecutive integer is (x+1).
\n" ); document.write( " $\"%28x%2B1%29%5E3+-+x%5E3+=+217\"$ Expand this.
\n" ); document.write( " $\"%28x%5E3%2B3x%5E2%2B3x%2B1%29-x%5E3+=+217\"$ Simplify.
\n" ); document.write( " $\"3x%5E2%2B3x%2B1+=+217\"$ Subtract 217 from both sides.
\n" ); document.write( " $\"3x%5E2%2B3x-216+=+0\"$ Factor the trinomial.
\n" ); document.write( " $\"3%28x%5E2%2Bx-72%29+=+0\"$
\n" ); document.write( " $\"x%5E2%2Bx-72+=+0\"$
\n" ); document.write( " $\"%28x-8%29%28x%2B9%29+=+0\"$
\n" ); document.write( " $\"x+=+8\"$ or $\"x+=+-9\"$
\n" ); document.write( "The two integers are 8 and 9
\n" ); document.write( "Check:
\n" ); document.write( " $\"9%5E3-8%5E3+=+729-512\"$ = $\"217\"$ \n" ); document.write( "

\n" );