Logical Solution in Maths

Maths can be solved in many ways, as one learning it knows.

There are the conventional techniques or methods type of solving.
You follow all the rules and laws, applying them diligently to solve the problem.
It is OK, not wrong.

However, sometimes by looking at the problem, you can twist a bit and deviate to use the "logical" method to short-cut the solving.

What do I mean?

Let's look at an example.

(This method of logical thinking is applied, especailly, in solving Partial Fraction.)

5 = A(x - 1) + B (x + 2)

Find A and B.

Conventional method ==> maybe simultaneous way.
Logical mehtod.....

Let x = 1, to eliminate the unknown A, and keeping the other unknown B.
5 = A(1 -1) + B (1 + 2)
==> 5 = 0 + 3B
==> B = 5 / 3 Get it?

Now to figure out getting A.
Let x = -2, to get rid of B.
5 = A(-2-1) + B(-2 + 2)
==> 5 = (-3) A + 0
==> A = - 5/3.

Finish. Short and sharp, and easy.

This is when you apply the logical part to maths solving.

Simple trick, right? Maths is Interesting. Don't forget this.
:-)