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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!

Guest Jan 30, 2022

2⁺⁰ Answers

+1223

+1

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

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

CubeyThePenguin Jan 30, 2022

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Thanks a lot

Guest Jan 30, 2022

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