SOLUTION: How do you find the averages of polynomials such as in this problem: If {{{1/x+1/y=1/z}}} and xy=z , what is the average of x and y?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you find the averages of polynomials such as in this problem: If {{{1/x+1/y=1/z}}} and xy=z , what is the average of x and y?      Log On


   

Question 86009This question is from textbook Barron's PSAT/NMSQT 2006/2007
: How do you find the averages of polynomials such as in this problem: If 1%2Fx%2B1%2Fy=1%2Fz and xy=z , what is the average of x and y? This question is from textbook Barron's PSAT/NMSQT 2006/2007

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/y=1/z and xy=z
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Add the left side of the equation to get:
(y+x)/xy = 1/z
Substitute z in place of xy to get:
(y+x)/z = 1/z
The numerators must be equal:
x+y=1
To get the average divide by 2:
(x+y)/2 = 1/2
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Cheers,
Stan H.




Cheers,
Stan H.