document.write( "Question 155016: What two consecutive integers have cubes that differ by 217? \n" ); document.write( "
Algebra.Com's Answer #114143 by checkley77(12844)\"\" \"About 
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(x+1)^3-x^3=217
\n" ); document.write( "x^3+3x^2+3x+1-x^3=217
\n" ); document.write( "3x^2+3x-216=0
\n" ); document.write( "(3x-24)(x+9)=0
\n" ); document.write( "3x-24=0
\n" ); document.write( "3x=24
\n" ); document.write( "x=24/3
\n" ); document.write( "x=8 for the amallernteger.
\n" ); document.write( "8+1=9 for the larger integer.
\n" ); document.write( "proof;
\n" ); document.write( "9^3-8^3=217
\n" ); document.write( "729-512=217
\n" ); document.write( "217=217
\n" ); document.write( " \n" ); document.write( "
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