SOLUTION: insert two geometric means between 6 and 162

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Question 81175This question is from textbook
: insert two geometric means between 6 and 162 This question is from textbook

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
insert two geometric means between 6 and 162
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Let x and y be the two geometric means:
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EQUATION:
6/x = x/y = y/162
Then you have two equation:
6y=x^2 and y^2=162x
Solve the 1st for y: y=x^2/6
Substitute into the 2nd to get:
(x^2/6)^2=162x
x^4 = 6^2*162x
x^4-36*162x=0
Factor:
x(x^3-5832)=0
x^3=5832
x=18
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Substitute that into y^2=162x to solve for y
y^2=162*18
y=54
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Then 6/18=18/54=54/162
18 and 54 are the two geometric means
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Cheers,
Stan H.