<PRE><B>Question 242957</B>
What are the dimensions of a box with NO top that is to be built if the combined area of the sides and bottom are going to be 68ft^2 and the volume is 32ft^3.

My futile attempt:

This question is in a chapter about nonlinear systems so i set up two equations.

{{{yx^2=32}}} (for the volume)
{{{4yx+x^2=68}}} (for the combined areas of the sides and bottom)

solved for y in first equation and substituted it into the second:

{{{4x(32/x^2)+x^2=68}}} simplifying I got {{{x^3-68x+128}}} and that is where i got stuck. Any suggestion would be greatly appreciated.
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2 is a zero of the cubic.
If yx^2 = 32, then y = 8
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You assume the bottom is square, it might not be.</PRE>