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Given that 

\(\frac{1}{x} + \frac{1}{y} = 5 \)

\(3xy + x + y = 4\)

 

compute \(x^2y+xy^2\)

 

Thanks in advance!

 Jan 30, 2022
 #1
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1/x + 1/y = 5

(x + y)/xy = 5

x + y = 5xy

 

3xy + x + y = 4

x + y = 4 - 3xy

 

5xy = 4 - 3xy

8xy = 4

xy = 1/2

 

\(x^2 y + xy^2 = (x+y)(xy) = 5(1/2)(1/2) = \boxed{5/4}\)

 Jan 30, 2022
 #2
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Thanks a lot

Guest Jan 30, 2022

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