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AS maths question - quadratics, curves, etc

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
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 323^2 and get a familiar quadratic in 3x3^x
(edited 6 years ago)
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tfpsa
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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 323^2 and get a familiar quadratic in 3x3^x


hmm, brilliant, let me try that...
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tfpsa
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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 323^2 and get a familiar quadratic in 3x3^x


did i really make an error there?
Original post by tfpsa
did i really make an error there?


3x−2(3x−10)=−13^{x-2}(3^x-10)=-1

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

⇏1−3x−2(3x−10)=0\not\Rightarrow 1-3^{x-2}(3^x-10)=0
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tfpsa
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Original post by RDKGames
3x−2(3x−10)=−13^{x-2}(3^x-10)=-1

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

⇏1−3x−2(3x−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???
(edited 6 years ago)
Original post by tfpsa
...


Yep. Other than that, my suggestion to multiply by 323^2 rather than 32−x3^{2-x} would've let you arrive at the quadratic in (slightly) fewer lines.
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tfpsa
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Original post by RDKGames
Yep. Other than that, my suggestion to multiply by 323^2 rather than 32−x3^{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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