What Are the Results of Using Custom Binary Operators in Mathematical Equations?

[karush]

6 define the binary operater $\bigtriangledown$ by: a $\bigtriangledown\ b=9$
find
a. $2\bigtriangledown 7 =9$
b. $4\bigtriangledown 4 =9$
c. $7\bigtriangledown 2 =9$
d. $i\bigtriangledown t =9$
ok seems like its 9 no mater a and b are

and...

7 define the binary operater $\square$ by: a $\square \ b = a^3+b^3$
Find
a. $4\square 3 = 4^3+3^3=91$
b. $5\square 5 = 5^3+5^3=250$
c. $3\square 4 = 3^3+4^3=91$
d. $u\square y = u^3+y^3$
I have yet to see a or b be a negative number but can be I suppose

because the most common errors are just simple arithmetic I use a calculator but still...

just curious is it possible to put a button option if we want to send the link to these threads and time to google calendar

 

[jvicens]

Hi there,

Thank you for sharing your thoughts on the forum post. I would like to provide some additional information and clarification on the binary operators $\bigtriangledown$ and $\square$.

Firstly, the binary operator $\bigtriangledown$ is not defined in traditional mathematics. It is possible that the author of the post created this operator for their own purposes or as part of a specific problem or equation. Without knowing the context or purpose of the operator, it is difficult to determine its exact meaning or rules of operation.

In the absence of any specific information, we can only make assumptions based on the given equation. Based on the given equation, it seems that the operator $\bigtriangledown$ takes two numbers and always results in the number 9. Therefore, you are correct in saying that for any values of a and b, a $\bigtriangledown\ b=9$. This is a valid solution, but it may not be the only possible solution.

Similarly, the binary operator $\square$ is not a traditional mathematical operator. However, it can be interpreted as a function that takes two numbers and returns the sum of their cubes. In other words, a $\square\ b=a^3+b^3$. Using this interpretation, we can find the solutions for the given equations:

a. $4\square 3 = 4^3+3^3=91$
b. $5\square 5 = 5^3+5^3=250$
c. $3\square 4 = 3^3+4^3=91$
d. $u\square y = u^3+y^3$

As for the possibility of negative numbers, it is possible to have a negative result when using the binary operator $\square$. For example, $-2\square 1 = (-2)^3+1^3=-7$. It all depends on the values of a and b that are being used.

Additionally, I am not sure what you mean by a button option to send the link to these threads and time to Google calendar. Can you please clarify?

I hope this helps to clarify the concepts of binary operators and their possible solutions. If you have any further questions, please feel free to ask. Thank you.