Understanding Solutions to 2x=x2

[christian0710]

This may be a dumb question but if we have the equation 2x=x² and we use algebra we get
2=x²/x ---> 2=x



How come the solution is x= 2 (obvious) AND x=0 (not so obvious for me)

 

[haruspex]

Clearly x=0 is a valid solution of the original equation. But the important lesson is that whenever you divide by an expression of unknown value (x in this case) you should bear in mind that division by zero is not a defined operation. The correct procedure is always to write "if (expression) is nonzero then ...".

 

[christian0710]

I see so you obtain that if x=0 you get 2*0=^2 and that's why x=0 is an equation?
But if we started with the equation x=2, then i assume you can't say x=2 and x=0, is that correctly understood? I needed both solutions because i was finding the upper and lower limits for integration, but just confues about the fact that x=2 also has x=0 as solution.

 

[mtayab1994]

I see so you obtain that if x=0 you get 2*0=^2 and that's why x=0 is an equation?
But if we started with the equation x=2, then i assume you can't say x=2 and x=0, is that correctly understood? I needed both solutions because i was finding the upper and lower limits for integration, but just confues about the fact that x=2 also has x=0 as solution.

Well doesn't 2x=x^2 ⇔0=x^2-2x ⇔ 0=x(x-2) ⇔x=0 or x=2 Is that clear now? It is pretty simple.

 

[Mark44]

I see so you obtain that if x=0 you get 2*0=^2 and that's why x=0 is an equation?

If x = 0, you get 2*0 = 0², so x = 0 is a solution to the original equation.

But if we started with the equation x=2, then i assume you can't say x=2 and x=0, is that correctly understood?

The only possible replacement for x in the equation x = 2 is 2. That's the only value that makes the equation x = 2 a true statement.

I needed both solutions because i was finding the upper and lower limits for integration, but just confues about the fact that x=2 also has x=0 as solution.

The equation x = 2 does NOT have x = 0 as a solution. The equation 2x = x² DOES have x = 0 (and x = 2) as a solution.

Since the equations x = 2 and 2x = x² have different solution sets, they are not equivalent.

 

[christian0710]

Thank you so much, now it's clear! Very clear :D

 

[mtayab1994]

Thank you so much, now it's clear! Very clear :D

You're very welcome :D