# Simple equation causing a lot of head ache

• Marin
In summary, the conversation is about a person trying to solve an equation but getting confused by the fact that a certain number is both a solution and no solution. They discuss the equation and try to solve it, but encounter issues with using exponent rules. They ask for help in identifying their mistake.
Marin
Hi there!

I was trying to solve an equation but got very perplexed by the fact that a certain number x=0 is both a solution and no solution:

Here´s the equation:

$$(x-a)[(x-a)^2+y^2+z^2]^{-3/2}+(x+a)[(x+a)^2+y^2+z^2]^{-3/2}=0$$

assume y=z=0:

Now, the equation becomes:

$$(x-a)[(x-a)^2]^{-3/2}+(x+a)[(x+a)^2]^{-3/2}=0$$

I guessed a solution at x=0

check: $$-a[(-a)^2]^{-3/2}+a[a^2]^{-3/2}=0$$, ok I assume it´s true

Now let´s use the exponent rule: (a^x)^y=a^(xy)

Then the equation becomes:

(*) $$(x-a)(x-a)^{-3}+(x+a)(x+a)^{-3}=0$$, or

$$(x-a)^{-2}+(x+a)^{-2}=0$$

Ok, plug once again x=0 and there coems the surprise:

$$(-a)^{-2}+(+a)^{-2}=1/a^2+1/a^2$$ is not equal to 0!

What is more, if you substitute x=0 before you contract the factors in (*) ypu come up with: $$(-a)^{-4}+(+a)^{-2}=1/a^4+1/a^2$$ again no 0, but also different from the result above!

I suppose I´m doing it somehow wrong woth the powers and exponents but I can´t figure it out!

If you see my mistake, please tell me!

Hi Marin!
Marin said:
… Now let´s use the exponent rule: (a^x)^y=a^(xy)

Sorry … doesn't always work, especially if y is a fraction and a is negative

## 1. What is a simple equation causing a lot of head ache?

The simple equation causing a lot of head ache is a mathematical equation that may seem easy to solve, but can become complex and difficult to understand or solve.

## 2. Why is this simple equation causing a lot of head ache?

This simple equation may be causing a lot of head ache because it involves multiple variables, complex operations, or a combination of both.

## 3. How can I solve this simple equation causing a lot of head ache?

The best way to solve a simple equation causing a lot of head ache is to break it down into smaller parts, use algebraic techniques, and practice solving similar equations to gain experience and improve problem-solving skills.

## 4. Are there any tips for solving this simple equation causing a lot of head ache?

Yes, some tips for solving a simple equation causing a lot of head ache include reading the question carefully, simplifying the equation by combining like terms, and using the correct order of operations.

## 5. What are some common mistakes people make when trying to solve a simple equation causing a lot of head ache?

Some common mistakes people make when trying to solve a simple equation causing a lot of head ache include forgetting to use the correct order of operations, not fully understanding the question, or making errors in calculations.

• General Math
Replies
9
Views
1K
• General Math
Replies
3
Views
1K
• General Math
Replies
2
Views
799
• General Math
Replies
7
Views
1K
• General Math
Replies
2
Views
757
• General Math
Replies
11
Views
904
• General Math
Replies
4
Views
1K
• General Math
Replies
4
Views
1K
• General Math
Replies
2
Views
1K
• General Math
Replies
2
Views
773