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    f(x) = (3-4√x)² / √x Show that f(x).. equals:

    9x^-1/2 + Ax1/2 + B where A and B are constants to be found.


    Not quite sure how t0 get that - since I got something completely different after expanding brackets etc...

    9 - 12 sprtx - 12 sprtx +16x / sprt x

    16x - 24sprtx +9 / sprt x


    Thats not going to look like how thay want it.... but not really sure what to do and the mark scheme doesnt give much away....
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    Well, (3-4√x)² expands to 9 - 24√x +16x and if you put that all over √x you get 9x^-1/2 (1/x = -1 so 1/√x = -1/2), -24 (-24√x/√x) = -24) and +16x^1/2 (16x/√x = 16x^1/2 ---- x^1 - x^1/2 = x^1/2) so if I've differentiatied it correctly, A would be 16 and B would be -24
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    (Original post by christinajane)
    f(x) = (3-4√x)² / √x Show that f(x).. equals:

    9x^-1/2 + Ax1/2 + B where A and B are constants to be found.


    Not quite sure how t0 get that - since I got something completely different after expanding brackets etc...

    9 - 12 sprtx - 12 sprtx +16x / sprt x

    16x - 24sprtx +9 / sprt x


    Thats not going to look like how thay want it.... but not really sure what to do and the mark scheme doesnt give much away....
    f\left(x\right)= \dfrac{\left( 3-4 \sqrt x \right)^2}{\sqrt x}

     \dfrac{9-12 \sqrt x - 12\sqrt x + \left( 4\times 4\right)\times \left(\sqrt x \times \sqrt x \right)}{\sqrt x}

    remember that  \sqrt x = x^{\frac {1}{2}}

    \dfrac {9-24\sqrt x +16x}{\sqrt x}
    Spoiler:
    Show
     9x^{\frac{1}{2}} -24 +16x^{\frac{1}{2}}

    done
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    (Original post by DrNippleson)
    Well, (3-4√x)² expands to 9 - 24√x +16x and if you put that all over √x you get 9x^-1/2 (1/x = -1 so 1/√x = -1/2), -24 (-24√x/√x) = -24) and +16x^1/2 (16x/√x = 16x^1/2 ---- x^1 - x^1/2 = x^1/2) so if I've differentiatied it correctly, A would be 16 and B would be -24


    Ahh I htink I get it now - each term is divided by that sprt x - because I was just bringing the sprt x up at the very end of the equation.

    This revising malarky is helping me out big time! haha forgetting little things like that!
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    (Original post by christinajane)
    Ahh I htink I get it now - each term is divided by that sprt x - because I was just bringing the sprt x up at the very end of the equation.

    This revising malarky is helping me out big time! haha forgetting little things like that!
    I've done the same in my mocks - just got to remember that divide is minus glad I could help
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    (Original post by christinajane)
    Ahh I htink I get it now - each term is divided by that sprt x - because I was just bringing the sprt x up at the very end of the equation.

    This revising malarky is helping me out big time! haha forgetting little things like that!
    Pretty much, all you're doing is that:

    \displaystyle 

\begin{equation*}\frac{a+b+c+d}{  e} = \frac{a}{e} + \frac{b}{e} + \frac{c}{e} + \frac{d}{e}\end{equation*}

    Etc... - obviously using the fact that \frac{a^n}{a^m} = a^{n-m} and \frac{1}{\sqrt{x}} = x^{-1/2}.
 
 
 
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