<PRE><B>Question 538762</B>
each edge of a cube is 2 cm longer than each edge of another cube. the volumes of the cubes differ by 98 cm cubed. 
can you find the lengths of the edges of each cube?
:
x = the edge of the smaller cube
then
x^3 = the volume
:
(x+2) = edge of the larger cube
then
(x+2)^3 = the volume
(x+2)*(x+2)*(x+2) = x^3 + 6x^2 + 12x + 8
:
Larger - smaller = 98 cub/cm
x^3 + 6x^2 + 12x + 8 - x^3 = 98
x^3 - x^3 + 6x^2 + 12x + 8 - 98 = 0
6x^2 + 12x - 90 = 0
simplify, divide by 6, results:
x^2 + 2x - 15 = 0
factors to
(x+5)(x-3) = 0
the positive solution
x = 3 cm is the length of the side of the small cube
then
5 cm is the length of the larger cube
:
:
Check this
5^3 = 125 cu/cm
3^2 =  27 cu/cm
----------------
diff: 98 cu/cm</PRE>