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

gigi9

Help plz!

How can I change this y=2/3x^(3/2)-1/2x^(1/2) in term of y, as x=...???

StephenPrivitera

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

Homework Helper
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))).

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

The easiest approach is not to square each side but instead to subsitute $$z = \sqrt{x}$$ which leads directly to the reduced cubic of,

$$4 z^3 - 3 z - 6 y = 0$$

gigi9

I have to solve the equation 2/3x^(3/2)-1/2x^(1/2) for "X", as x=....

HallsofIvy

Homework Helper
Yes, that was what you said before and you got three replies telling you how to do that.

StephenPrivitera

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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