Respuesta :
We will have the following:
First, we know that the volume of a rectangular prism has the form:
[tex]V=l\cdot h\cdot w[/tex]So, we will factor the expression, that is:
[tex]V=x^3y+xy^3-2x^2y^2\Rightarrow V=xy(y^2-2x+x^2)[/tex][tex]\Rightarrow V=xy((x-y)(x-y))\Rightarrow V=xy(x-y)^2[/tex]Since the base is a square we will have that the only candidate for it to be is "x*(x - y)^2 " or "y*(x - y)^2". If x*y where the base, then the expression would equal "0". This is since the base is an square, then x = y, so (x - y)^2 = (x - x)^2 = 0; or (y - y)^2 = 0.
Then: We will have that the lateral area will be given by "xy", that is:
[tex]4xy=30[/tex]Now, we solve for either "x" or "y" in this last expression, that is:
[tex]y=\frac{15}{2x}[/tex]From the problem we will also have that:
[tex]V=w\cdot h\cdot l=w^2\cdot h=l^2\cdot h[/tex]So:
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