document.write( "Question 551403: A positive number is 3 more than twice another number. the difference of their squares is 24. find the two integers. (algebraic solutions only) \n" ); document.write( "

Algebra.Com's Answer #359735 by KMST(5347) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the greater number be x and the lesser number be y.
\n" ); document.write( " $\"x=2y%2B3\"$ , so $\"x%3E2y%3Ey%3E0\"$
\n" ); document.write( "Since $\"x%3Ey%3E0\"$ , of course $\"x%5E2%3Ey%5E2%3E0\"$ .
\n" ); document.write( " $\"x%5E2-y%5E2=24\"$
\n" ); document.write( "Substituting $\"x=2y%2B3\"$ into $\"x%5E2-y%5E2=24\"$ , we get
\n" ); document.write( " $\"%282y%2B3%29%5E2-y%5E2=24\"$ --> $\"4y%5E2%2B12y%2B9-y%5E2=24\"$ --> $\"3y%5E2%2B12y-15=0\"$ --> $\"y%5E2%2B4y-5=0\"$ --> $\"%28y-1%29%28y%2B5%29=0\"$
\n" ); document.write( "The positive solution is $\"y=1\"$ . (We ignore solution $\"y=-5\"$ because we know y is positive).
\n" ); document.write( "Then $\"x=2y%2B3=2%2A1%2B3=2%2B3=5\"$
\n" ); document.write( "So the two integers are 1 and 5. \n" ); document.write( "

\n" );