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Demand Functions

I need some help checking my work on the following problems. I essentially worked out to where I took both of the partials and wrote in terms of L, but I need some help with the algebra to get through the next few steps.

Using the budget constraint I=PxX + PyY ....find the demand for goods x and y. Set up as a Langrangian of the form u(x,y) + L (I-PxX-PyY)

A) u(x,y) (x-2) (y-3)

I worked up to the point where:

L = Y-3 / Px = X-2 / Py

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B) u(x,y) = X ^ 2/3 Y

Over here I worked up until

L = 2/3 (X)^ -1/3 Y / Px = (X) ^2/3 / Py

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C) U(x,y)=Sqrt (x) Sqrt(y)

I worked up to

L= 1/2 x ^ - 1/2 y ^1/2 / Px = 1/2 x ^ 1/2 y ^ -1/2 / Py

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