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    Hi there, really struggling with the below, wondered if anyone has any pointers for this two-part question. It's meant to be one of the 'hard' ones at the end of a question set.

    (a) Solve the equation x2-10x+9= 0

    This seems fairly straightforward, it factorises (x-9),(x-1), x= 9 or 1.

    (b) Hence or otherwise solve the equation 3x-2(3x-10)=-1

    I badly struggled here. Presumably I need to restate the second equation so it's in a very similar form to the first one, but I drew a big blank. Being honest I'm probably a little sketchy on my rules of indices but that's not the only problem..

    Obviously I'll need to get everything on one side, e.g.

    1 - 3x-2(3x-10) = 0

    And then i guess multiply everything by some kind of "x squared" term...

    I thought about multplying everything by 32-x... giving me something like (see above for comment on rules of indices)...

    32-x - 30(3x-10)=0

    32-x - 3x+10=0

    ...

    this just looks nothing like the first equation... any tips??? thanks
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    (Original post by tfpsa)
    Obviously I'll need to get everything on one side, e.g.

    1 - 3x-2(3x-10) = 0
    Error straight away, this is not the same as what you started with.

    After that just multiply by 3^2 and get a familiar quadratic in 3^x
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    (Original post by RDKGames)
    Error straight away, this is not the same as what you started with.

    After that just multiply by 3^2 and get a familiar quadratic in 3^x
    hmm, brilliant, let me try that...
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    (Original post by RDKGames)
    Error straight away, this is not the same as what you started with.

    After that just multiply by 3^2 and get a familiar quadratic in 3^x
    did i really make an error there?
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    (Original post by tfpsa)
    did i really make an error there?
    3^{x-2}(3^x-10)=-1

    \Rightarrow 1+3^{x-2}(3^x-10)=0

    \not\Rightarrow 1-3^{x-2}(3^x-10)=0
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    (Original post by RDKGames)
    3^{x-2}(3^x-10)=-1

    \Rightarrow 1+3^{x-2}(3^x-10)=0

    \not\Rightarrow 1-3^{x-2}(3^x-10)=0
    duh, yep.

    so i did this & then something really cack handed

    multplying everything by 32-x.

    32-x + 30(3x-10)=0


    32-x +3x-10=0


    maybe then multiply by 3x


    32+(3x)2-10(3x) = 0



    Let 3x = A



    A2-10A+9 = 0



    A = 9 or 1

    so 3x = 9 or 1

    x = 2 or 0???
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    (Original post by tfpsa)
    ...
    Yep. Other than that, my suggestion to multiply by 3^2 rather than 3^{2-x} would've let you arrive at the quadratic in (slightly) fewer lines.
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    (Original post by RDKGames)
    Yep. Other than that, my suggestion to multiply by 3^2 rather than 3^{2-x} would've let you arrive at the quadratic in (slightly) fewer lines.
    great, thanks vv much. i'm not great at this stuff. you're right, 32 is quicker.
 
 
 
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