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# Algebra

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Given that 1/x + 1/y = 5, 3xy + x + y = 4 + x + y, compute x^2*y + x*y^2.

Feb 14, 2022

#1
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First I simplified the first equation to:

x + y = 5xy. I got this by multiplying both sides of the equation by 'xy'.

Then we can substitute that into the second equation, getting:

3xy + 5xy = 4 + 5xy.

This simplifies to 3xy = 4.

And xy = 4/3.

Since the question is looking for x^2y + xy^2, that is equal to: (x+y)(xy).

Substituting the value back in, we have (5xy)(xy), and finally:

$$x^2y + xy^2 = {80\over9}$$

Feb 14, 2022