Homework Help

What is root of equation 6*9^(1/x)-13*6^(1/x)+6*4^(1/x)=0?

user profile pic

yapayapa | (Level 2) Honors

Posted July 14, 2013 at 5:30 PM via web

dislike 0 like

What is root of equation 6*9^(1/x)-13*6^(1/x)+6*4^(1/x)=0?

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 14, 2013 at 5:38 PM (Answer #1)

dislike 1 like

The root of the equation `6*9^(1/x)-13*6^(1/x)+6*4^(1/x)=0` has to be determined.

`6*9^(1/x)-13*6^(1/x)+6*4^(1/x)=0`

=> `6*3^(2/x)-13*3^(1/x)*2^(1/x)+6*2^(2/x)=0`

Let `3^(1/x) = X` and `2^(1/x) = Y`

=> `6*X^2 - 13*X*Y + 6*Y^2 = 0`

=> `(2*Y-3*X)*(3*Y-2*X) = 0`

2*Y-3*X = 0

=> `Y/X = 3/2`

=> `(2/3)^(1/x) = 3/2`

=> `1/x = -1`

=> x = -1

`3*Y-2*X = 0`

=> 3*Y = 2*X

=> `Y/X = 2/3`

=> `(2/3)^(1/x) = 2/3`

=> `1/x = 1`

=> x = 1

The solution of the given equation is x = 1 and x = -1

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes