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Find all values of x that satisfy 6(x + 1/x)^2 - 35(x + 1/x) + 50 = 0.

 Dec 15, 2019

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 #1
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"Find all values of x that satisfy 6(x + 1/x)^2 - 35(x + 1/x) + 50 = 0."

 

First let y = x + 1/x.  Then we have  6y^2 -35y + 50 = 0  Solve this using the quadratic equation, to get two values of y.

 

Then set x + 1/x equal to each value of y in turn, multiply through by x each time to get another quadratic (this time in x) and solve for x.  

 

You will get four values of x in total.

 Dec 15, 2019
 #1
avatar+29200 
+5
Best Answer

"Find all values of x that satisfy 6(x + 1/x)^2 - 35(x + 1/x) + 50 = 0."

 

First let y = x + 1/x.  Then we have  6y^2 -35y + 50 = 0  Solve this using the quadratic equation, to get two values of y.

 

Then set x + 1/x equal to each value of y in turn, multiply through by x each time to get another quadratic (this time in x) and solve for x.  

 

You will get four values of x in total.

Alan Dec 15, 2019

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