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What is the length of the edge of a cube if its volume could be doubled by an increase of 6 centimeters in one edge, an increase of 12 centimeters in a second edge, and a decrease of 4 centimeters in the third edge
\n" ); document.write( ":
\n" ); document.write( "Let x = the length of the cube featured here
\n" ); document.write( "then
\n" ); document.write( "x^3 = the volume of this cube
\n" ); document.write( "and
\n" ); document.write( "2x^3 = twice the volume
\n" ); document.write( ":
\n" ); document.write( "(x+6)*(x+12)*(x-4) = 2x^3
\n" ); document.write( "FOIL
\n" ); document.write( "(x^2 + 12x + 6x + 72)*(x-4) = 2x^3
\n" ); document.write( "(x^2 = 18x + 72)*(x-4) = 2x^3
\n" ); document.write( "Multiply
\n" ); document.write( "x^3 + 14x^2 - 288 = 2x^3
\n" ); document.write( "x^3 - 2x^3 + 14x^2 - 288 = 0
\n" ); document.write( "-x^3 + 14x^2 - 288 = 0
\n" ); document.write( "Just the sign of x^3 was changed, therefore we know that two of the factors of this equation: (x-6) and (x-12)
\n" ); document.write( ":
\n" ); document.write( "Check x=6 as the side of the original cube
\n" ); document.write( "Find the original volume 6^3 = 216 cu/units
\n" ); document.write( "Find the new volume:
\n" ); document.write( "(6+6)*(6+12)*(6-4) =
\n" ); document.write( "12 * 18 * 2 = 432 cu/units, twice the volume of 216
\n" ); document.write( ":
\n" ); document.write( "Do the same with x=12
\n" ); document.write( "Find the original volume 12^3 = 1728 cu/units
\n" ); document.write( "Find the new volume:
\n" ); document.write( "(12+6)*(12+12)*(12-4) =
\n" ); document.write( "18 * 24 * 8 = 3456 cu/units, twice the volume of 1728
\n" ); document.write( ":
\n" ); document.write( "we have two solutions for x, 6 and 12 \n" ); document.write( "