document.write( "Question 825271: The difference between 2 natural numbers is 4.The sum of their squares is greater than 9 times sum by 8.Find the numbers \n" ); document.write( "
Algebra.Com's Answer #497209 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "The difference between 2 natural numbers is 4.The sum of their squares is greater than 9 times sum by 8.Find the numbers \r
\n" ); document.write( "\n" ); document.write( "

\n" );
document.write( "Let the larger and smaller of the 2 numbers be L, and S, respectively
\n" );
document.write( "Then: L - S = 4______L = 4 + S ----- eq (i)
\n" );
document.write( "Also, \"L%5E2+%2B+S%5E2+=+9%28L+%2B+S%29+%2B+8\" 
\n" );
document.write( "      \"L%5E2+%2B+S%5E2+=+9L+%2B+9S+%2B+8\"
\n" );
document.write( "      \"L%5E2+%2B+S%5E2+-+9L+-+9S+-+8+=+0\"---- eq (ii)
\n" );
document.write( "      \"%284+%2B+S%29%5E2+%2B+S%5E2+-+9%284+%2B+S%29+-+9S+-+8+=+0\" ------ Substituting 4 + S for L in eq (ii)
\n" );
document.write( "      \"16+%2B+8S+%2B+S%5E2+%2B+S%5E2+-+36+-+9S+-+9S+-+8+=+0\"
\n" );
document.write( "      \"S%5E2+%2B+S%5E2+%2B+8S+-+9S+-+9S+%2B+16+-+36+-+8+=+0\"______Collecting like-terms
\n" );
document.write( "      \"2S%5E2+-+10S+-+28+=+0\"______Combining like-terms
\n" );
document.write( "      \"2%28S%5E2+-+5S+-+14%29+=+2%280%29\")______Factoring out GCF, 2
\n" );
document.write( "      \"S%5E2+-+5S+-+14+=+0\"
\n" );
document.write( "      (S + 2)(S - 7) = 0
\n" );
document.write( "      S = - 2               OR                 S = 7 
\n" );
document.write( "Since - 2 is NOT a natural number, the smaller of the 2 natural numbers is: \"highlight_green%287%29\"\r
\n" );
document.write( "\n" );
document.write( "L = 7 + 4 ------ Substituting 7 for S in eq (i) 
\n" );
document.write( "L = 11, so the larger of the 2 natural number is: \"highlight_green%2811%29\"
\n" );
document.write( "You can do the check!! \r
\n" );
document.write( "\n" );
document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
\n" );
document.write( "Further help is available, online or in-person, for a fee, obviously. \r
\n" );
document.write( "\n" );
document.write( "For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams, 
\n" );
document.write( "GENERAL MATH QUESTIONS, MATH HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra,
\n" );
document.write( "Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE, GRE, CLEP,
\n" );
document.write( "and the GED, you can visit: http://asvabstudyzone.freeforums.net/. \n" );
document.write( "
\n" );