document.write( "Question 253639: what three digit number made of consecutive digits is 2 less than a cube and 2 more than a square \n" ); document.write( "

Algebra.Com's Answer #186002 by drk(1908) $\"\"$ $\"About$

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Let htu be a three digit number. Since the numbers are consecutive, we have h_h-1_h-2
\n" ); document.write( "in decreasing form or
\n" ); document.write( "h_h+1_h+2 in increasing form.
\n" ); document.write( "--
\n" ); document.write( "decreasing order will not produce any answers.
\n" ); document.write( "--
\n" ); document.write( "increasing :
\n" ); document.write( "This can be expressed as h(100) + (h+1)(10) + h+2. Now\r
\n" ); document.write( "\n" ); document.write( "(i) S^2 + 2 = h(100) + (h+1)(10) + h+2
\n" ); document.write( "(ii) S^2 = 100h +11h + 10
\n" ); document.write( "(iii) S^2 = 111h + 10
\n" ); document.write( "If h = 1, then
\n" ); document.write( "S^2 = 111 + 10 = 121
\n" ); document.write( "S = 11.
\n" ); document.write( "The number is 123
\n" ); document.write( "--
\n" ); document.write( "(v) h(100) + (h+1)(10) + h+2 = s^3 - 2
\n" ); document.write( "(vi) 100h +11h + 14 = S^3
\n" ); document.write( "(vii) 111h + 14 = S^3
\n" ); document.write( "If h = 1, then
\n" ); document.write( "S^3 = 111 + 14 = 125
\n" ); document.write( "S = 15.
\n" ); document.write( "The number is 123. \n" ); document.write( "

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