Finding unknown constants

• Jan 7th 2011, 01:29 AM
Glitch
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.
• Jan 7th 2011, 01:40 AM
Random Variable
You can expand the stuff on the right and then equate like terms. You'll get a system of equations.
• Jan 7th 2011, 01:41 AM
FernandoRevilla
Quote:

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
• Jan 7th 2011, 01:46 AM
TheCoffeeMachine
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. :)
• Jan 7th 2011, 01:49 AM
Random Variable
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 \$.
• Jan 7th 2011, 02:01 AM
FernandoRevilla
Quote:

Originally Posted by TheCoffeeMachine
EDIT: Oops! Ah, well! I'm too slow, I guess. :)

Welcome to the Club. :)

Fernando Revilla
• Jan 7th 2011, 03:26 AM
Glitch
Thanks. This thread is proof that obvious things often dodge my thinking process!