document.write( "Question 1109206: a number is one less than twice another number,and the difference between their squares is 85. find the numbers \n" ); document.write( "
Algebra.Com's Answer #724207 by ankor@dixie-net.com(22740)\"\" \"About 
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a number is one less than twice another number,
\n" ); document.write( "a = 2b - 1
\n" ); document.write( "and the difference between their squares is 85.
\n" ); document.write( "a^2 - b^2 = 85
\n" ); document.write( "replace a with (2b-1)
\n" ); document.write( "(2b-1)^2 - b^2 = 85
\n" ); document.write( "FOIL (2b-1)(2b-1)
\n" ); document.write( "4b^2 - 2b - 2b + 1 - b^2 = 85
\n" ); document.write( "Combine to form a quadratic equation on the left
\n" ); document.write( "3b^2 - 4b + 1 - 85 = 0
\n" ); document.write( "3b^2 - 4b - 84 = 0
\n" ); document.write( "you can use the quadratic formula; a=3; b=-4; c=-84, but this will factor
\n" ); document.write( "(3b+14)(b-6) = 0
\n" ); document.write( "The positive integer solution
\n" ); document.write( "b = 6
\n" ); document.write( "Find a
\n" ); document.write( "a = 2(6) - 1
\n" ); document.write( "a = 11
\n" ); document.write( ":\r
\n" ); document.write( "\n" ); document.write( " find the numbers 11, 6
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check:
\n" ); document.write( "11^2 - 6^2 =
\n" ); document.write( "121 - 36 - 85 \n" ); document.write( "
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