document.write( "Question 889419: find two consecutive psitive odd numbers which are such that the he sum square of their sum exceeds the sum of their square by 26. \n" ); document.write( "
Algebra.Com's Answer #538226 by ankor@dixie-net.com(22740)\"\" \"About 
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I could not get an integer solution with a difference of 26
\n" ); document.write( "a difference of 30 or of 70, yields integer solutions
\n" ); document.write( "Solving this problem
\n" ); document.write( "find two consecutive positive odd integers such that their sum squared, exceeds the sum of their squares by 30.
\n" ); document.write( ":
\n" ); document.write( "Let x = the odd number
\n" ); document.write( "then
\n" ); document.write( "(x+2) = the next odd number
\n" ); document.write( "therefore
\n" ); document.write( "(2x+2) = the sum of these two numbers
\n" ); document.write( ":
\n" ); document.write( "(2x+2)^2 - (x^2 + (x+2)^2) = 30
\n" ); document.write( "FOIL
\n" ); document.write( "4x^2 + 8x + 4 - (x^2 + x^2 + 4x + 4) = 30
\n" ); document.write( "4x^2 + 8x + 4 - x^2 - x^2 - 4x - 4 = 30
\n" ); document.write( "combine like terms, to form a quadratic equation
\n" ); document.write( "2x^2 + 4x - 30 = 0
\n" ); document.write( "simplify, divide by 2
\n" ); document.write( "x^2 + 2x - 30 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x+5)(x-3) = 0
\n" ); document.write( "The positive solution
\n" ); document.write( "x = 3
\n" ); document.write( "therefore the two consecutive odd numbers
\n" ); document.write( "3, 5
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this
\n" ); document.write( "8^2 - (3^2 + 5^2) =
\n" ); document.write( "64 - 34 = 30 \n" ); document.write( "
\n" );