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    Its Q 10 on page 139 Mixed Exercise 9D in Edexcel C2 Book:

    10) The diagram shows part of the curve with equation y = 5 - 1/2x^2 for which y> (greater than or equal to) 0.
    The point P(x,y) lies on the curve and O is the origin.

    a) show that OP^2 = 1/4x^4 -4x^2 + 25

    I kinda understand this question - but can someone please explain to me where the -4x^2 comes from?

    Using pythagoras - and even the distance formula I get -

    op^2 = x^2 + (5-1/2x^2)^2

    Which I always get as :

    op^2 = x^2 + 25 +1/4x^4

    Dont know where that -4x^2 seems to come from....

    I know this is gonna be really obvious..
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    (Original post by christinajane)
    ...
    Hey! Sounds like you've forgotten how to expand brackets. Remember that:

    \displaystyle 

\begin{equation*}(a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ba + b^2 = a^2 + ab + b^2\end{equation*}

    So in your case, when you expand:

    \displaystyle

\begin{equation*} \left(5 - \frac{x^2}{2}\right)^2 = \left(5 - \frac{x^2}{2}\right)\left(5 - \frac{x^2}{2}\right) = 5\left(5 - \frac{x^2}{2}\right) - \frac{x^2}{2}\left(5 - \frac{x^2}{2}\right) = \cdots \end{equation*}

    Can you take it from there?

    Basically, when you square brackets, you do (a+b)^2 = a^2 + 2ab + b^2.

    So in your case it's:

    \displaystyle 

\begin{equation*}\left(5 - \frac{x^2}{2}\right)^2 = (5)^2 + 2\left(5\right)\left(-\frac{x^2}{2}\right) + \left(\frac{x^2}{2}\right)^2\end  {equation*}

    For now, I would recommend that whenever you see things like (a+b)^2, write it out explicitly as (a+b)(a+b) and then expand that as you normally would with two brackets. Over time, you'll get used to it and you'll be able to write out the squared brackets in its final form without needing to worry about the intermediate step of writing the two brackets next to each other.
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    Argh yes!! Oh my god - I know it would be ridiculously obvious and I know that you normally expand brackets when there is a ^2 to the side of a bracket!

    How stupid of me - my face is very red.

    Its late her - so and not much sleep last night so - I like to think thats the reason ive been so stupid right now!

    haha - oh dear...
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    (Original post by christinajane)
    Argh yes!! Oh my god - I know it would be ridiculously obvious and I know that you normally expand brackets when there is a ^2 to the side of a bracket!

    How stupid of me - my face is very red.

    Its late her - so and not much sleep last night so - I like to think thats the reason ive been so stupid right now!

    haha - oh dear...
    It's not stupid at all, in fact, it's such a common mistake that it's been given a name: Freshmans dream. It is very late where I am as well (2 a.m) so I fully understand what you mean! Time for bed, perhaps. :-)
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    Yes definitely time for bed!

    I feel better now that I know that sort of mistake has a name! :-)
 
 
 
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