Find 3 Real Solutions

[dougr.]

Note the symmetry of you replace x by minus x in this equation, in either form

[GDPlainA]

x³=x
x³-x=0
Factoring x out (not dividing),
x(x²-1)=0
Using differences of squares in the parentheses,
x(x+1)(x-1)=0

x=-1, 0, or 1

[mihael]

That is so simple, I never would have thought of that!

[datra]

I'd love practical examples of these equations.

[gabriel]

Neat! Thank you from a GED holder who never had the chance to fall in love with math.

[jaxonkruz]

I went to one right away, I never considered the other two

[dougr.]

Easy by inspection, but analytic method is best

[dougr.]

Easy peasy if you have seen his other videos. factorizability matters!

[PatrickPease]

I knew the answer, but I don't know how to discover the answer. I don't know how you get from x(x²+1)(x²-1)=0 to the three options without simply knowing it.

[YouTubeism.]

Equation : x(x+1)(x-1) = 0
Finding real solutions
→ x = 0/[(x+1)(x-1)] = 0,
→ x+1 = 0/[x(x-1)] = 0 (2)
x = -1,
→ x-1 = 0/[x(x+1)] = 0,
x = 1

Values of X are 0, ±1

If x = 0, then how it can be divided by 0 on RHS? It should be undefined 🤔
Here it is From (2), eq : x+1 = 0/[x(x-1)]
Substituting x = 0 in the given eq.
We get 0+1 = 0/[0(0-1)]
1 = 0/0
???

I'm confused, Can anyone please explain?

[TristanLoh]

Is it correct if I divide both sides by x?

[sandybristow]

Even though I’m lost af I still 😢 math lol

[hilmanh.]

Sir, why when you have thing like that, we cant just divide each side so we got x² instead of x³ - x? Is it because we must got three solution?

[NothingMaster]

You showed the solutions algebraically which is the orthodox/formal way of approaching a problem like this. And obviously there is no problem with that. But you could also find the solutions using intuitive reasoning/substitution knowing that the only way X^3 = X could be true is if X was 0. 1, or -1; where the -1 solution is associated with the power of 3.

[Tcrrxzz]

At first I thought it was something like 1 or 0 and then I found out -1 was a valid answer

[aidannt]

I genuinely love the way you teach and the way you can write on the board without looking 🤯. I have great respect for you sir 🫡.

[oz]

If the equation has three answers, does this not make it invalid? x

[mrreemann]

Now plug in a number for X.
If X = 3 Are you telling me
27 = 3. ????

[NAcHO-wxvg]

I at first only got 1 and 0 and couldn’t remember what the third number was, then remembered… -1 cubed is -1

[thelonewolf]

obvious. I was just typing something extremely dumb and I realized that I am mistaken. Of course 0 is part of the solution.