# Thread: Finding unknown constants

1. ## Finding unknown constants

The question

Find the constants A, B and C for:

$\displaystyle x^2 + 3 = A(x + 1)^2 + B(x - 1)(x + 1) + C(x - 1)$

My attempt
I tried to isolate the constants by substituting strategic values of x. For example:

Let x = -1,
C = -2

Let x = 1,
A = 1

However, I cannot isolate B. I'm sure this question is trivial and my brain is still in holiday mode. Any assistance would be most welcome.

2. You can expand the stuff on the right and then equate like terms. You'll get a system of equations.

3. Originally Posted by Glitch
Let x = -1, C = -2 Let x = 1, A = 1
Right. Now, substitute (for example) $\displaystyle x=0$ and find $\displaystyle B$ .

Fernando Revilla

4. Put $\displaystyle x = 0$ and use the values of A and C which you have already found to get B.
Zero is just convenient - any constant apart from those which you have used will do.

EDIT: Oops! Ah, well! I'm too slow, I guess.

5. Or you could take the derivative of both sides and get $\displaystyle 2x = 2A(x+1) + B(x+1) + B(x-1) + C$, substitute $\displaystyle x = -1$, and see that $\displaystyle C = 0$.

6. Originally Posted by TheCoffeeMachine
EDIT: Oops! Ah, well! I'm too slow, I guess.
Welcome to the Club.

Fernando Revilla

7. Thanks. This thread is proof that obvious things often dodge my thinking process!