More Conjectures

[braincrampgeo]

Here is another one of the completing the conjecture. Can you please explain how you get the answer for this one? Thank you.

The direction state: complete the conjecture based on the pattern you observe in the specific cases

problem:

The product of a number (n-1) and the number (n+1) is always equal to __?__

3*5= 4^2-1
4*6=5^2-1
5*7=6^2-1
6*8=7^2-1
7*9=8^2-1
8*10=9^2-1

 

[mmm4444bot]

A conjecture is a guess.

In mathematics, most conjectures are educated guesses.

So, if you examine the products listed in this exercise, do you recognize any similarities between them?

In other words, compare the following expressions, and try to find something they all share in common.

4^2 - 1
5^2 - 1
6^2 - 1
7^2 - 1
8^2 - 1
9^2 - 1

Once you find something that they all share in common, then try to be more specific by relating individual results to the factors that generated them. Doing this allows you to fill in the blank more precisely.

If you want more help with this exercise, then please post what you discovered during your examination.

 

[Deleted member 4993]

Where is 3 & 5 on the number line compared to 4?

Where is 4 & 6 on the number line compared to 5?

The right-hand-side is a difference of squares. Can you factorize that?

and so on...

answers to these questions will guide you to the correct conjecture.