C2 Revision Watch

Esquire
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#21
Report 13 years ago
#21
alpha m8... u missed the point C2 level question= C2 level maths. vazzy i like ur style, but theres a simpler way and you dont have to make your own simultaneous equations.... you are right though, using logs on this question is like swatting a fly with a sledge hammer.
a^x=b^y=(ab)^xy
take either a^x=(ab)^xy or b^y=(ab)^xy and also a^x=b^y (no need for b=a^(x/y))
so... a^x=(ab)^xy ... for argument's sake
a^x=(a^xy)(b^xy) now... b^y=a^x
a^x=(a^xy)(a^(x^2))
a^x=a^(xy + x^2)
x=xy + x^2
1=y+x as required.
if you use b^y=(ab)^xy you will get the same result. Really this is quite simple indices... the kind of thing you should get at GCSE.
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Fade Into Black
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#22
Report 13 years ago
#22
can i just say:

a^x=(a^xy)(b^xy) now... b^y=a^x
a^x=(a^xy) (a^(x^2))

when you swap b^xy for a^x
you are left with b^x . a^x

how did you get a^x=(a^xy)(a^(x^2)) ????

apologies if i have missed some basic aspect, hopefully someone can point out my stupid mistake.
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Dekota
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#23
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#23
(Original post by V.P. Keys)
Call it being pedantic if you must, but here we have;

y² + xy = y, you factorise first:
=> y(y+x) = y, then you divide:
=> y + x = 1
I don't know why some members are against my amendment here. I've simply factorised and then divided. What is so hard about putting the extra step in your working?

I mean c'mon two people against me? They don't have the right to call themselves mathematicians if they don't have the will to improve their maths and accept the truth.
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Christophicus
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#24
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#24
(Original post by V.P. Keys)
I don't know why some members are against my amendment here. I've simply factorised and then divided. What is so hard about putting the extra step in your working?

I mean c'mon two people against me? They don't have the right to call themselves mathematicians if they don't have the will to improve their maths and accept the truth.
The point is, it's so blatently obvious that you can divide all terms in the equation by y, I thought there was no need for a step such as that.
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Dekota
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#25
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#25
(Original post by Widowmaker)
The point is, it's so blatently obvious that you can divide all terms in the equation by y, I thought there was no need for a step such as that.
Be honest; it's not about how obvious it was, it was that you just get so used to these things that you have that tendency to miss out steps because you "just know them". But when demonstrating to someone else, you should show these steps, it's essentially good practice to.

A suggestion rather than criticism was intended.
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AlphaNumeric
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#26
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#26
But the point if you don't have to do that line. True, you can, but is it truely nessacery to put in every single step you do in a new line? It doesn't make it any more "true" doing for. For instance you said
y² + xy = y, you factorise first:
=> y(y+x) = y, then you divide:
=> y + x = 1
while if you put in every bit of arithmetic you should have done

y² + xy = y, you swap the order of x and y, so the y is to the left of x
y² + yx = y, now you can pull out y to the left so give
=> y(y+x) = y, then you multiply by 1/y
=> 1(y + x) = 1
=> 1y + 1x = 1
=> y + x = 1

That is going through every single step you actually need to do, but most people accept xy = yx and that 1*y = y and 1*x = x, so don't bother typing out such arithmetic. The same applies for cancelling through by y when it is obvious every quantity is a multiply of y. Missing out that step doesn't make it any less true. Sure, some derivations require more steps than others before they are complicated, but I give people enough credit to notice that y², yx and y are all multiples of y, don't you?

As for calling ourselves mathematicians, to quote Professor Timothy Gowers, a Fields Medalist, and Cambridge lecturer, "The notion of a Hilbert space sheds light on so much of modern mathematics, from number theory to quantum mechanics, that if you do not know at least the rudiments of Hilbert space theory then you cannot claim to be a well educated mathematician". Something tells me I know a fair bit more about Hilbert spaces and their applications than you and I value Prof Gowers' view of my mathematical ability a bit more than I view your opinion of my maths.
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