SOLUTION: The aritimetic mean of two numbers is 5 and the geometric mean is 4. Which of the following are the numbers? Indicate all correct options.

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Question 790409: The aritimetic mean of two numbers is 5 and the geometric mean is 4. Which of the following are the numbers? Indicate all correct options.
Answer by mananth(16946) About Me  (Show Source):
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let the numbers be x & y
(x+y)/2 = 5
x+y=10

GM = sqrt(xy)
4 = sqrt(xy)
16 = xy
16/y =x
16/y + y =10
multiply by y
16+y^2=10y
y^2-10y+16=0
y^2-8y-2y+16=0
y(y-8)-2(y-8)=0
(y-8)(y-2)=0
y = 8 OR y=2
when y = 8 x=2
when y = 2 x=8