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The volumes of two cubes differ by 259 cu meters.
\n" ); document.write( " If the edges of one cube are each 4 meters greater than the edges of the other,
\n" ); document.write( "what is the sum of the lengths of one edge of each cube?
\n" ); document.write( ":
\n" ); document.write( "Let x^3 = vol of the smaller cube
\n" ); document.write( "then
\n" ); document.write( "(x+4)^3 = vol of the larger
\n" ); document.write( ":
\n" ); document.write( "Large cube vol - small cube vol = 259 cu/m
\n" ); document.write( "(x+4)^3 - x^3 = 259
\n" ); document.write( ":
\n" ); document.write( "(x+4)(x^2 + 8x + 16) - x^3 = 259
\n" ); document.write( ":
\n" ); document.write( "x^3 + 12x^2 + 48x + 64 - x^3 = 259
\n" ); document.write( ":
\n" ); document.write( "Fortunately the x^3's cancel and we can form a quadratic equation
\n" ); document.write( "12x^2 + 48x + 64 - 259 = 0
\n" ); document.write( ":
\n" ); document.write( "12x^2 + 48x - 195 = 0
\n" ); document.write( ":
\n" ); document.write( "Simplify divide by 3
\n" ); document.write( "4x^2 + 16x - 65 = 0
\n" ); document.write( ":
\n" ); document.write( "Factor this to
\n" ); document.write( "(2x - 5)(2x + 13) = 0
\n" ); document.write( ":
\n" ); document.write( "Positive solution
\n" ); document.write( "2x = +5
\n" ); document.write( "x = 2.5 meters is the edge of the smaller cube
\n" ); document.write( "then
\n" ); document.write( "2.5 + 4 = 6.5 meters is the edge of the larger
\n" ); document.write( ":
\n" ); document.write( "\"what is the sum of the lengths of one edge of each cube?\"
\n" ); document.write( "2.5 + 6.5 = 9 meters
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check solution on a calc; enter 6.5^3 - 2.5^3 = 259 \n" ); document.write( "