Maths question- A level help please

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Voss.gloss20
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Hey,

The question asks:

a) Solve the equation: x^2-10x+9=0

Which I got x=9 and x=1

b) Hence, or otherwise, solve the equation

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

I'm struggling with part b.

Thanks,
V
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RandomGuest
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Expand and use a suitable substitution for 3^x
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RDKGames
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(Original post by Voss.gloss20)
Hey,

The question asks:

a) Solve the equation: x^2-10x+9=0

Which I got x=9 and x=1

b) Hence, or otherwise, solve the equation

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

I'm struggling with part b.

Thanks,
V
Make a substitution y = 3^x so that this equation becomes

\dfrac{y}{9}(y-10) = -1
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Voss.gloss20
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(Original post by RDKGames)
Make a substitution y = 3^x so that this equation becomes

\dfrac{y}{9}(y-10) = -1
Thank you. How would I know in the future to out y=3x rather than y=3x-2 for example?
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mqb2766
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(Original post by Voss.gloss20)
Thank you. How would I know in the future to out y=3x rather than y=3x-2 for example?
The sub y=3^x is the most natural and gives the part a) equation directly. So it would be the one to try first so the word "hence" in the question.

y=3^(x-2)=3^x/9 would give
y(9y-10)=-1
or
9y^2 - 10y + 1 = 0
which is similar, and gives the same result in the end (for x=...), but its less obvious how to use the part a, so the "or otherwise" in the question.
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Voss.gloss20
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(Original post by mqb2766)
The sub y=3^x is the most natural and gives the part a) equation directly. So it would be the one to try first so the word "hence" in the question.

y=3^(x-2)=3^x/9 would give
y(9y-10)=-1
or
9y^2 - 10y + 1 = 0
which is similar, and gives the same result in the end (for x=...), but its less obvious how to use the part a, so the "or otherwise" in the question.
Ohh right. Thanks
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