You should be able to solve this problem (standard for high school students in the U.S.S.R)

>when you post /leftypol/ memes in a math thread

[math]\sqrt(107+\sqrt(107+x))=x[/math]
[math]107+\sqrt(107+x)=x^2[/math]
[math]107+x=(x^2-107)^2[/math]
[math]107+x=x^4 -214x^2+107^2[/math]
[math]x^4-214x^2-x+11342=0[/math]
Okay, but seriously: how do you get the root algebraically?

There's a general equation for 4th order polinomials, but not even the most autustic fucks in HS know it by heart (one usually looks at these problems from galois theory). So maybe there's some stupid trick involved like looking at it like a fixed point problem or some clever substitution but who cares?

I hope this is a bait troll thread . The answer is a nested square root.

Sqrt(107+sqrt(107+sqrt(107+sqrt(107+...))))

The number of nested squart roots the closer to the answer you get.

>square both sides
>subtract 107 on both sides
>square both sides again
>subtract (107+x) on both sides
>left with 4th order polynomial in standard form
>use numerical methods to find roots (newton's method, etc) or software like wolframalpha, Matlab etc
yawn*

[math]x = \frac{1+\sqrt{429}}{2}[/math]

I think the point is that it's giving as a classroom exercise. Everything can be solved numerically ffs, but most of the time people don't care about that.

>doing commie maths

what's wrong with his eye...

This is basically right, no? If x satisfies sqrt(107+x)=x, then obviously
sqrt(107+sqrt(107+x))=x

There is only one solution because sqrt(107+sqrt(107+x))-x is monotone decreasing for x>0.

Ok then as an alternative to numerical, you can substitute x^2=y and solve with quadratic equation. It is a trick i learned in 10th grade algebra at a ghetto SoCal public school.

forgot my yawn*

You have an odd power you retard. Solving higher order polynomials is not trivial.

Proof:
Suppose P=NP
Then P/N=P
So P must equal 0 but thats not true so P=/=NP
QED

The trick is the realize why the starting equation implies the second equation.

Bujt of course the positive value is the true x

the trick is to realize that the 2nd implies the 1st, so a solution to the second gives a solution to the first.

conservatives triggered by math yet again

10.832 + x^1/2 = x

You should be able to solve this:
Kilograms of bread required > Kilograms of bread available

x~~10.856

Import grain from U.S.A.

Resorting to numerical methods.

How does it imply that?

If you plug in that equation into x in the original and plug it in into the new x you’ll see that it’s the same thing it’s recursive so it doesn’t matter which one you use

Wow very interesting,

on a totally unrelated subject, i've noticed that every if you put all digits from 1 to 9 in whatever order you like (every number only used once), it is always divisable by 9. Is there a way to prove this for all possible permutations?
This also works for 1 to 8, 0 to 8, 0 to 9.

yes

That's cool as fuck.

>Solved by inspection
[math]
x \approx 10.86
[/math]
Work smarter, not harder

Wrong, the first doesn't imply the second, it has solutions other than the one you solved for.
Although once you have that you can just do some polynomial division and reduce the rest of the problem to another 2nd degree to find the rest of the roots.

...

Soviet textbooks are weird
Problem 1 is showing classical result like the sum of an arithmetical series, then you devolve into 10-page long calculations

I like Landau&Lifchitz as much as the next guy but don't try to do the problems in a first lecture, you'll lost your mind

Sexy solution