Power of Using "Let" to Simplify Maths Solving

Anyone doing maths may encounter instances where the expressions are long and seemingly complex.

Example 1: 3(logx)² + 4 logx + 5 = 1

Example 2: 3(1/x)² + 4(1/x) + 5 = 1

When you jump straight into them, trying to solve them, you may encounter confusion, if inexperience with the working.

However, there is simple way to resolve this issue.

Since the mathematical expressions are complex to the eye, you can actually "simplify" them visually.

Make sure that doing any simplification, the meaning of the maths question should not change.

One technique to simplify the expression is to use "Let".

What do I mean?

Let's take the above examples to task.

Example 1: Let y = log x
The "complex" expression now becomes ==> 3 y² + 4y + 5 = 1

Example 2: Let y = 1/x
The equation becomes also ==> 3 y² + 4y + 5 = 1

See the usefulness of the technique here.

This technique is easy and familiar to anyone having learned simple algebra.
The above two expressions have been reduced to the familiar quadratic equations.

The only extra steps to complete the solution is the conversion back to find x.
This is so, since, solving the simplified equations give you the answer to "y", not x.

Thus, you have only to revert the "y" back to x through y = log x and y 1/x respectively.

Easy isn't it?
Maths is easy and interesting, if you want it to be.

:-)