SOLUTION: 2(y)^1/9 - 3 (y)^1/18 + 1 = 0 I've got it broken down to (2y^1/18 -1)(y^1/18 - 1) = 0 I'm confused as to what the next step is and how to get there! Thanks so much, Trac

Algebra ->  Inequalities -> SOLUTION: 2(y)^1/9 - 3 (y)^1/18 + 1 = 0 I've got it broken down to (2y^1/18 -1)(y^1/18 - 1) = 0 I'm confused as to what the next step is and how to get there! Thanks so much, Trac      Log On


   

Question 501818: 2(y)^1/9 - 3 (y)^1/18 + 1 = 0
I've got it broken down to
(2y^1/18 -1)(y^1/18 - 1) = 0
I'm confused as to what the next step is and how to get there!
Thanks so much,
Tracy
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
2(y)^1/9 - 3 (y)^1/18 + 1 = 0
I've got it broken down to
(2y^1/18 -1)(y^1/18 - 1) = 0
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To avoid working with fractional exponents, let x = y^(1/18)
Then we can rewrite the equation as:
2x%5E2+-+3x+%2B+1+=+0
This can be factored as:
(2x-1)(x-1) = 0
The solutions are x = 1/2, x = 1
Therefore 1 = y^(1/18) -> y = 1
For the other root, 1/2 = y^(1/18)
To solve for y raise both sides to the 18th power:
(1/2)^18 = y
So the two roots are 1 and (1/2)^18