Elementary Equation solving mind-block

  • Thread starter truewt
  • Start date
78
0
Hi I have some problems with really basic equations (really elementary)

Let's say in order to solve an equation [TEX]f(x)=0[/TEX], we multiply the equation by [TEX]x[/TEX]. Therefore we conclude that x can never be =0. But what if at the end step we conclude that [TEX]x=0[/TEX] (maybe along with other solutions)? Do we reject the answer and accept the others? Or is our method of solving the equation incorrect?

I do know that it is quite impossible for you to arrive at [TEX]x=0[/TEX] after you multiply [TEX]x[/TEX] throughout in order to solve the equation, as that would mean you had introduced an unnecessary common multiple into the equation..
 

HallsofIvy

Science Advisor
Homework Helper
41,715
876
Hi I have some problems with really basic equations (really elementary)

Let's say in order to solve an equation f(x)=0, we multiply the equation by x. Therefore we conclude that x can never be =0.
Why would we conclude that?

But what if at the end step we conclude that x=0 (maybe along with other solutions)? Do we reject the answer and accept the others? Or is our method of solving the equation incorrect?

I do know that it is quite impossible for you to arrive at x=0 after you multiply x throughout in order to solve the equation, as that would mean you had introduced an unnecessary common multiple into the equation..
I'm not at all clear what you are saying here. Certainly if you just take an arbitrary equation, say x2= 0, and multiply both sides by x, you can arrive at x= 0: x3= 0 so x= 0. You may be thinking of an equation in which you have good reason to multiply by x- say something like (x-1)/x= 0. In that case, even before you multiply by x, you know that x= 0 cannot be a solution.
It is well known that if you multiply both sides of an equation by any function of x, you may introduce "extraneous" roots: numbers that satisfy the new equation but not the original. The only way to be sure is to check the numbers in the original equation.
 
78
0
Alright thanks. Sorry for not visiting this thread after so long.
 

Related Threads for: Elementary Equation solving mind-block

Replies
4
Views
3K
  • Posted
Replies
12
Views
2K
Replies
43
Views
12K
  • Posted
Replies
5
Views
2K
  • Posted
Replies
2
Views
1K
  • Posted
Replies
4
Views
1K
  • Posted
Replies
2
Views
1K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top