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#1 2006-05-26 02:22:23
- thinkdesigns
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Why is this true
at a basic GCSE level, i am stuggling with this concept
(3x-b)^2 - 9 = ax^2-12x+c
find a,b and c for all values of x
i was told taht
9x^2 -6xb+b^2 - 9=ax^2-12x + c
therefore, a must equal 9 b must equal minus 2
this emans that the equation falls nicely into place
then when x=0
b^2 - 9=c
substituting that in
-5=c
however, i argued that there was more than one solution and actually, becuase there is 4 variables, and only 1 equation, it is impossible to figure all the equation out with numbers
e.g c could equal anything, and this would balance out any differences, meaning that a,b or c could be anything
why am i wrong?
#2 2006-05-26 02:56:45
- numen
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Re: Why is this true
a can only be 9 because the x² must match on both sides since you have an equal sign, thus b can only be 2 due to the same reason with x, which reduces the number of variables to 2. On the left side of the equation you still have b²-9, which should be c according to the right side. With the already known b=2, c becomes -5. So the only variable you got left is x.
a, b and c can only equal 9, 2 and -5 respectively, anything else wouldn't solve the equation. This is if a, b and c is not a function of x, of course, and just numbers.
Bang postponed. Not big enough. Reboot.
#3 2006-05-27 01:19:52
- thinkdesigns
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Re: Why is this true
thanks, you have cleared things up alot, so it works, as long as each one is an actual number and not a function of x, that was the thing that kept catching me out, i simply couldn't see how it worked, but the assumption has to be made that it is not a function of x
#4 2006-05-27 03:35:54
- numen
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Re: Why is this true
If a, b or c is a function of x, it is usually written a(x), b(x) or c(x). 
Bang postponed. Not big enough. Reboot.