#1**0 **

**(x + y)/2 = 5 **

**sqrt(xy) = 3**

sqrt(xy)^{2}=3^{2} Square both sides to eliminate the square root on the left side.

xy = 9

(xy)/x = 9/x Divide x on both sides.

y = 9/x

Now that you know y, you can solve for x by using the first equation given.

**(x + y)/2 = 5 **

(x+(9/x))/2 = 5 Substitute 9/x into the value of y.

(x+(9/x))/ 2 ⋅ 2 = 5 ⋅ 2 Multiply 2 on both sides to get rid of the denominator on the left side.

x+(9/x) = 10

x+(9/x) - x = 10 - x Subtract x on both sides.

9/x = 10 - x

(9/x) ⋅ x = (10 - x) ⋅ x Multiply x on both sides to get rid of the denominator once again.

9 = 10x - x^{2}

9 - 9 = 10x -x^{2} -9 Subtract 9 to move everything onto one side.

-x^{2} +10x - 9 = 0 Rewrite.

-1 (-x^{2} +10x - 9 = 0) From here, we must factor to get the values of x. But first we must mulitply the equation by -1.

x^{2} - 10x + 9 = 0 Factor.

(x+10) (x-1) = 0 Now set each of the parenthesis to equal 0.

x + 10 = 0

x = -10

x - 1 = 0

x = 1

auxiarc May 31, 2020

#2**+1 **

\({(x+y)\over 2} =5\)

\( \sqrt{xy} =3\)

\(xy = 9\)

\(x = {9\over y}\)

\({({{9\over y}+y)}\over 2} = 5\)

\({({{9\over y}+y)}} =10\)

\({({{9\over y}+{y^2\over y})}} =10\)

\({9+y^2} = 10y\)

\((y-9)(y-1) = 0\)

\(y = 1\)

\(x = 9\)

\(y = 9\)

\(x = 1\)

.Hephaestus May 31, 2020