Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

#1 2006-05-26 02:22:23

thinkdesigns
Member

Offline

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
Full Member

Offline

Re: Why is this true

a can only be 9 because the x 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 b-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
Member

Offline

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
Full Member

Offline

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). smile


Bang postponed. Not big enough. Reboot.
 

Board footer

Powered by FluxBB