(adsbygoogle = window.adsbygoogle || []).push({}); Assumed solution for the Laplace EQUATION??

The book I'm using says that the method of separation of variables is a must when solving the Laplace equation. OK, well they ASSUME that the solution looks like

V(x,y,z)=X(x)*Y(y)*Z(z)

but why can't they assume a solution of

V(x,y,z)=X(x) + Y(y) + Z(z)?????

When performing the[itex]\nabla \bullet [/itex]([itex]\nabla[/itex]V)operation, the difference is that their assumed solution leads to[1/X(x)]* d, while what I'm proposing will lead to just^{2}[X(x)]/dx^{2}= -k_{x}^{2}d^{2}[X(x)]/dx^{2}= -k_{x}^{2}

Since what I'm proposing is easier, why would that be the one used?

Thanks.

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# Assumed solution for the Laplace EQUATION?

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