SOLUTION: Hello, I would like to find help in HOW to solve a quadratic equation such as the one listed below. I am not quite sure on how to work the fractional powers. I have tried the quadr
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-> SOLUTION: Hello, I would like to find help in HOW to solve a quadratic equation such as the one listed below. I am not quite sure on how to work the fractional powers. I have tried the quadr
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Question 1008619: Hello, I would like to find help in HOW to solve a quadratic equation such as the one listed below. I am not quite sure on how to work the fractional powers. I have tried the quadratic equation but that does not work out and I have tried seeing it as 9(x^(1/3))^2-26x^(1/3)-3=0. I have seen youtube videos on how to solve equations in quadratic with fractional powers but most factor nicely and I cannot seem to get my problem to do so as well. I would really appreciate some assistance with this problem.
9x^(2/3)-26x^(1/3)-3=0
The standard method solving equations like this is as follows.
Introduce new variable
y = x^(1/3) = (1).
Then your equation takes the form
- - = . (2)
It is a quadratic equation for y. Solve it using the quadratic formula:
= = = .
Thus the equation (2) has two solutions: = 3; = .
Now, to find x, you need solve two equations ( recall (1) ):
1) = 3. To solve it, raise both side to the degree 3: x = = 27.
2) = . To solve it, raise both side to the degree 3: x = = .
Answer. There are two solutions of the original equation: x = 27 and x = .