small help .

[strong crane]

$x=\frac{1}{2-\frac{1}{2-\frac{1}{2-x}}}}$

[fair walrus]

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[storm jetty]

Infinite.......
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fossil swallow]

hmmm

ig you just isolate x

oh it's an infinite fraction

well, isolate x

[hollow parcel]

Lmao

It's not really infinite

Although you can solve it as if it was

[fossil swallow]

$x = \frac{1}{2-\frac{1}{\frac{3-2x}{2-x}}}$

[storm jetty]

Inverse Cupid #GTFOanemia

[strong crane]

No, it's finite

[fossil swallow]

$x = \frac{1}{2-\frac{2-x}{3-2x}}$

[storm jetty]

Inverse Cupid #GTFOanemia

[strong crane]

It is given that x≠2

[frail heron]

Isn't this the same as : $\ x=\frac{1}{2-x}$

[storm jetty]

Ludwig

[strong crane]

I thought there is any tricks..

What's your answer?

[fossil swallow]

$x = \frac{1}{\frac{4-3x}{3-2x}}$

[storm jetty]

Inverse Cupid #GTFOanemia

[fossil swallow]

$x = \frac{3-2x}{4-3x}$

[storm jetty]

Inverse Cupid #GTFOanemia

[strong crane]

4x-3x²=3-2x

[fossil swallow]

$-3x^2 + 4x = 3 - 2x$

[storm jetty]

Inverse Cupid #GTFOanemia

[strong crane]

I thought there is any tricks like assuming anything.....

[fossil swallow]

$3x^2 - 6x + 3 = 0$

[storm jetty]

Inverse Cupid #GTFOanemia

[hollow parcel]

More or less

Yes

[fossil swallow]

$3x^2 - 3x - 3x + 3 = 0$

[storm jetty]

Inverse Cupid #GTFOanemia

[frail heron]

ok^^

[hollow parcel]

Not exactly

[strong crane]

X=1

[fossil swallow]

$3x(x-1)-3(x-1)$

[storm jetty]

Inverse Cupid #GTFOanemia

[fossil swallow]

yeah

[strong crane]

There isn't any short method?

[dreamy tusk]

That’s a way to go. I would have inverted the first equation first, etc. Your method would not work for a continued fraction

[hollow parcel]

Doing what Ludwig said

[fossil swallow]

idk tbh

oh yeah

what ludwig said

that'll work

[hollow parcel]

Your question is "equivalent" to $\ x=\frac{1}{2-x}$

[storm jetty]

Miguel

[strong crane]

Like , $\frac{2}{x}+ \frac{2}{3y}$ here we assume $$\frac{1}{x}$$ as. U or any variable

[fossil swallow]

no that's linear eq in 2 variables

[storm jetty]

Infinite.......

[fossil swallow]

over here just do what ludwig said

[strong crane]

No, I thought that we can assume like this in that question

[fossil swallow]

it works (somehow)

[strong crane]

Ludwig?

What did he say ?

[fossil swallow]

$x = \frac{1}{2-x}$

[storm jetty]

Inverse Cupid #GTFOanemia

[fossil swallow]

credits to Ludwig

[strong crane]

Oh, understood it .

Wait two minutes

I have one more question

[frail heron]

It is like saying : $\ x=\frac{1}{2-x} \$ is similar to $\ x=\frac{1}{2-\frac{1}{2-...}}$

[storm jetty]

Ludwig

[strong crane]

Ohk

[fossil swallow]

I must get off now

[hollow parcel]

That's what you also through at the start when you said that it was infinite

[fossil swallow]

bye!

[hollow parcel]

Bye!

[strong crane]

Wait , I have a question

[fossil swallow]

yeah but i didn't think it would work

oh well

[strong crane]

Yes

[fossil swallow]

bye!

[strong crane]

Found it

$\sqrt{x+\sqrt{x+....}}=6$

[storm jetty]

Infinite.......

[strong crane]

Find x

[hollow parcel]

Yeah

So as $\sqrt{x+....}=6$

[storm jetty]

Miguel

[hollow parcel]

You can substitute that in

[frail heron]

tricky

[hollow parcel]

$\sqrt{x+6}=6$

[storm jetty]

Miguel

[strong crane]

Yes...

[hollow parcel]

Now square both sides

Subtract 6 from both sides

[strong crane]

x=30

[hollow parcel]

And take square root in both sides

Not quite

[strong crane]

?

[hollow parcel]

Oh yes

Sorry sorry

Yes

[strong crane]

Wait let me see the answer in the book

Yes , correct

Thanks

@hollow parcel thanks

[left osprey]

@strong crane has given 1 rep to @forest temple

[strong crane]

+close