3=0

[unoduetre]

[mention=705]Tearmoon[/mention]

Which step do you think is wrong? The second step is just substitution. Or you mean finding x from the equation is wrong?

[unoduetre]

x² + x + 1 = 0
x² + x + 1 = 0

Step 1: Divide both sides of the first equation by x (x does not equal 0).

(x² + x + 1)/x = 0/x
x² + x + 1 = 0

Step 2: Simplify the first equation.

(x²)/x + x/x + 1/x = 0
x² + x + 1 = 0

Step 3: Further simplify the first equation.

x + 1 + 1/x = 0
x² + x + 1 = 0

Step 4: Subtract x² from both sides of the second equation.

x + 1 + 1/x = 0
x² + x + 1 - x² = 0 - x²

Step 5: Rearrange and simplify the second equation.

x + 1 + 1/x = 0
x² - x² + x + 1 = - x²

Step 6: Simplify the second equation.

x + 1 + 1/x = 0
x + 1 = - x²

Step 7: Subtract 1 from both sides of the second equation.

x + 1 + 1/x = 0
x + 1 - 1 = - x² - 1

Step 8: Simplify the second equation.

x + 1 + 1/x = 0
x = - x² - 1

Step 9: Substitute x in the first equation based on the second equation.

(- x² - 1) + 1 + 1/x = 0

Step 10: Simplify.

- x² - 1 + 1 + 1/x = 0

Step 11: Simplify.

- x² + 1/x = 0

Step 12: Add x² to both sides.

- x² + 1/x + x² = 0 + x²

Step 13: Reorder and simplify.

- x² + x² + 1/x = x²

Step 14: Simplify.

1/x = x²

Step 15: Reorder.

x² = 1/x

Step 16: Multiply both sides by x.

x² · x = (1/x) · x

Step 17: Simplify.

x³ = 1

Step 18: Take a cubic root from both sides.

x = 1

Step 19: Substitute x in the original equation.

1² + 1 + 1 = 0

Step 20: Simplify.

1 + 1 + 1 = 0

Step 21: Simplify.

3 = 0

---

So which step is wrong?

[Citizen]

I just checked on a calculator it said 3=3.

[unoduetre]

Damn, the calculator must be broken or something.

[unoduetre]

There is no error in the calculations! You're just afraid to admit that 3=0!!!!!

If there is an error, point it out! Otherwise accept it!

[Tanya]

This conclusion is incorrect.

The method used is a fallacy.

3 objects because math as you stated is 0 objects is not correct.

There are still 3 objects math cannot make it zero objects.

This just means this math with it's steps has a logical error in how the answer was found, thus the method utilized does not work in this instance and a different method must be used instead.

[unoduetre]

If that's the case, where is the error?

[Tanya]

The method used is the error.

There is no logical reason to look further into why the incorrect conclusion is the result.

Since the conclusion can be identified that it is in incorrect, a different method to come to the correct conclusion is needed.

[unoduetre]

You're just avoiding it. Psychological denial!!!




(I'm obviously joking of course. Yes, there is an error, but can you find it?)

[Tanya]

I probably could, but the calculations I'm dealing with at work that I need to find a solution for currently is tiresome as is. Perhaps after I'm finish dealing with that and finding a solution to it, I'll look at this one in detail.

[unoduetre]

Sure, no worries. I think it might be eye-opening, if you do it.

[unoduetre]

Well, I can give you a hint, so you don't waste time. All steps from 1 to 21 are correct.

[Tanya]

logical errors are something I deal with a lot with the type of work I do.

[unoduetre]

(By "correct" I mean each step from 1 to 21 is a correctly applied mathematical operation as applied to the result of the previous step. So you don't need to waste your time checking that.)

(One of the 21 steps is a bit tricky though, but not really incorrect.)

[Tanya]

I'll check it out later.