document.write( "Question 321696: Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number \n" ); document.write( "

Algebra.Com's Answer #230399 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Three consecutive whole numbers are such that the square of the middle number
\n" ); document.write( " is greater than the product of the other two by 1.
\n" ); document.write( " Find the middle number:
\n" ); document.write( "There is no unique solution
\n" ); document.write( ":
\n" ); document.write( "let x = the middle number
\n" ); document.write( "then
\n" ); document.write( "(x-1) = the 1st number
\n" ); document.write( "and
\n" ); document.write( "(x+1) = the 3rd number
\n" ); document.write( ":
\n" ); document.write( "x^2 = ((x-1)*(x+1)) + 1
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 = x^2 - 1 + 1
\n" ); document.write( ":
\n" ); document.write( "x^2 = x^2
\n" ); document.write( "Which means this is true for any 3 consecutive numbers even, -1, 0 +1
\n" ); document.write( ":
\n" ); document.write( "Try a few like; 142, 143, 144: 143^2 = 20449, 142*144 = 20448
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