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Given that
\(\begin{align*} \frac{1}{x}+\frac{1}{y}&=5,\\ 3xy+x+y&=4, \end{align*}\)
compute \(x^2y+xy^2\).

 Jan 26, 2021
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1/x +  1/y  = 5

 

(x + y)  / xy  = 5

 

x + y  =  5xy

 

3xy   + x + y  =  4

 

3xy  +  5xy   =  4

 

8xy =  4

 

xy  = 4/8 = 1/2

 

So

 

x^2 y + xy^2   =

 

xy  ( x + y)  =  

 

(1/2)  ( 5xy)  =

 

(1/2)  ( 5 * (1/2) )  =

 

5/4

 

 

cool cool cool

 Jan 26, 2021
edited by CPhill  Jan 26, 2021

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