Question

the real numbers x and y are such that x + 2/y = 8/3 and y + 2/x = 3. the value of xy is​

Answer 1

Answer:

value of xy is 2. See the solution and you will get it.

Answer 2

The value of xy is 2.

Step-by-step explanation:

Given : Equation $x+\frac{2}{y}=\frac{8}{3}$ and $y+\frac{2}{x}=3$

To find : The value of xy ?

Solution :

Equation 1 ,  $x+\frac{2}{y}=\frac{8}{3}$

Equation 2,  $y+\frac{2}{x}=3$

Multiply equation 1 and 2,

$(x+\frac{2}{y})(y+\frac{2}{x})=\frac{8}{3}\times 3$

$(\frac{xy+2}{y})(\frac{xy+2}{x})=8$

$(xy+2)(xy+2)=8xy$

$(xy)^2+2xy+2xy+4=8xy$

$(xy)^2-4xy+4=0$

$(xy)^2-2\times 2\times xy+(2)^2=0$

$(xy-2)^2=0$

$xy-2=0$

$xy=2$

Therefore, the value of xy is 2.

#Learn more

If xy=2 and xy^2=8 what is the value of x

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