How can I change this y=2/3x^(3/2)-1/2x^(1/2)

  • Thread starter gigi9
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Help plz!

How can I change this y=2/3x^(3/2)-1/2x^(1/2) in term of y, as x=...???
 
I hate fractions, so multiply through by 6. Factor out x1/2 on the right. Square each side. Expand the squared terms, distribute the x, subtract 36y2 from each side and apply the cubic formula (I don't know what it is but I know it exists).
 

HallsofIvy

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StephenPrivitera was assuming you meant

y= (2/3)x^(3/2)-(1/2)x^(1/2).

What you wrote could as easily be interpreted as

y= 2/(3x^(3/2)-1/(2x^(1/2))).

Please use parentheses to make your meaning clear.

In a bit more detail, what he said was: multiply the equation by 6 to get
6y= 4x^(3/2)- 3x^(1/2)= (4x- 3)x^(1/2)
so
36y^2= (4x-3)^2(x)= (16x^2- 24x+ 9)x
= 16x^3- 24x^2+ 9x

Which you can write as 16x^3- 24x^2+ 9x- 36y^2= 0 and solve as a cubic equation.

(You can see I have absolutely nothing to do this morning. Well, nothing I want to do!)
 

uart

Science Advisor
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The easiest approach is not to square each side but instead to subsitute [tex]z = \sqrt{x}[/tex] which leads directly to the reduced cubic of,

[tex] 4 z^3 - 3 z - 6 y = 0 [/tex]
 
41
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I have to solve the equation 2/3x^(3/2)-1/2x^(1/2) for "X", as x=....
 

HallsofIvy

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Yes, that was what you said before and you got three replies telling you how to do that.
 
Originally posted by HallsofIvy
StephenPrivitera was assuming you meant

y= (2/3)x^(3/2)-(1/2)x^(1/2).

What you wrote could as easily be interpreted as

y= 2/(3x^(3/2)-1/(2x^(1/2))).
I always assume calculator syntax if it's unclear.
 

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