SOLUTION: (6x-5)^2/3 = x^1/3 I have no idea what to do.

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Question 210762: (6x-5)^2/3 = x^1/3
I have no idea what to do.
Found 2 solutions by stanbon, tutor_paul:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
(6x-5)^2/3 = x^1/3
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Raise both sides to the 3rd power to get:
(6x-5)^2 = x
Expand:
36x^2 - 60x + 25 = x
36x^2 - 61x + 25 = 0
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Solve using the quadratic formula.
Then check your answers and eliminate extraneous zeroes.
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Cheers,
Stan H.
Answer by tutor_paul(519)   (Show Source): You can put this solution on YOUR website!
OK.. first step is not to panic :-)
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Next step is remember some laws about exponents. Namely that:

You can apply that to the left side of the equation:


Now square that binomial:

Cube both sides of the equation:

Equate to zero:

This is looking much more manageable now. just apply the quadratic formula to this and you are done:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=121 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1, 0.694444444444444. Here's your graph:



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Good Luck,
tutor_paul@yahoo.com
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