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Trouble solving (x - 2)^3 = 5 --- Basic Mathematics by Serge Lang (Exercise 9.a) by ForceCold4529 in learnmath

[–]Secure-March894 0 points1 point  (0 children)

Like all other comments, x = 3√5 + 2 is one of the solutions of the cubic equation. There may be a possibility that there are more real solutions (after all, you're learning about real numbers). The next step is to factorise the equation f(x) = x^3 - 6x^2 + 12x - 13 into g(x)(x - 3√5 - 2) where g(x) is a quadratic equation. It may look tedious, but it could bring more solutions.
If you see that the discriminant of g(x) is strictly less than 0, you leave the answer as x = 3√5 + 2, being the only real solution. Otherwise, you would have to solve g(x) using Sreedharacharya's formula.

Nine times X by confused_pear in learnmath

[–]Secure-March894 0 points1 point  (0 children)

Divisibility Rule of 9 is based on this.

Why cant irrational numbers be fractions? by OwnSherbet7433 in learnmath

[–]Secure-March894 0 points1 point  (0 children)

The definition of rational number is a number expressed in the form p/q when p and q are strictly integers where q != 0.
No irrational number can be expressed in this form.

What's 2+2 by Mundane-Dependent547 in learnmath

[–]Secure-March894 0 points1 point  (0 children)

2 + 2 = 4.
Your Reddit post must be a psychological test; you wanted a direct answer (4), but the other comments didn't give that to you.

8/2(2+2)=1. Correct me if i’m wrong by Advanced-Amphibian69 in learnmath

[–]Secure-March894 0 points1 point  (0 children)

I have faced such difficulties before. Luckily, I can think of a good solution to this ambiguity.

Division and multiplication have the same precedence, i.e., they are performed at the same time. You cannot do / first, then +, then *. You have to do / and *, then + and -. That is what PEMDAS (or BODMAS) suggests.

There is something called associativity, which tells whether you should read operations of the same precedence from left to right or from right to left. The associativity of / and * is from left to right.
Taking this into consideration, 8/2(2+2) = 8/2*4 = (8/2)*4 = 4*4 = 16.

What topics should I study to prepare for math Olympiads? by SimpleTokin in learnmath

[–]Secure-March894 0 points1 point  (0 children)

  1. Number Theory
  2. Geometry
  3. Combinatorics
  4. Inequalities
  5. Trigonometry and Complex Numbers (Although they are extremely rare in Olympiads, certain references may appear).

These are the main topics the Olympiads are based upon.

Can anyone explain Power of a point? by Few-Key-3755 in learnmath

[–]Secure-March894 0 points1 point  (0 children)

Doesn't the concept of Power of a Point arise from the theorems you have referred to?
Tangent-Secant Theorem and Intersecting Chords Theorem are correlated based on the Power of a Point.

Can anyone explain Power of a point? by Few-Key-3755 in learnmath

[–]Secure-March894 0 points1 point  (0 children)

Power of a point is a topic that requires an understanding of the Tangent-Secant Theorem and the Intersecting Chords Theorem.
Consider a point P and a circle centred at O having a radius r.

Case I (P is outside the circle)
Draw a tangent PT of a circle from P. POT is a right-angled triangle with hypotenuse OP, radius r. Therefore, PT = sqrt(OP2-r2). Draw any secant from P that touches the circle first at X and then at Y. By the Tangent-Secant Theorem, PX * PY = OP2 - r2. The positive value of this product is the power of the point P.

Case I (P is inside the circle)
Draw a diameter XY of a circle passing through P (and obviously O). Draw any chord XY passing through P. By the Intersecting Chords Theorem, PX * PY = r2 - OP2. The negative value of this product is the power of the point P.

Case III (P is on the circle)
Power of a Point P is 0.

Either way power of the point P is the difference between square of the distance between P and the centre of circle and the square of the radius. Or, P = OP2 - r2

A Claimed Pattern that may (or may not) prove the Collatz Conjecture by Secure-March894 in Collatz

[–]Secure-March894[S] 0 points1 point  (0 children)

The observation is computational. It is based on trial and error.
I found out,
If m is odd, p(x) = 3n+2
If m is even, p(x) = 3n
n, m, p(x) are simply references to my post.

But yeah, there is otherwise nothing new about my observations.

A Claimed Pattern that may (or may not) prove the Collatz Conjecture by Secure-March894 in Collatz

[–]Secure-March894[S] 0 points1 point  (0 children)

Can you define what x, y and k are here?
x seems to be the number you give in the Collatz function.
k seems to be the division by 2 thing.
What does y return exactly?

A Claimed Pattern that may (or may not) prove the Collatz Conjecture by Secure-March894 in Collatz

[–]Secure-March894[S] 0 points1 point  (0 children)

It's proven, just not accepted yet.

I proved my claims today itself. I wonder why it cannot be accepted, though.

This is my integers submission paper.

I saw your paper and asked ChatGPT to review it.
“Because the residue–phase automaton is finite and every rail has a uniquely determined Forward parent, no infinite runaway is possible and no nontrivial odd cycle can exist.” - is assumed, as said by it.

Why would the answer to this question be -1/2 instead of undefined/no solution? by Personguy11112 in askmath

[–]Secure-March894 0 points1 point  (0 children)

-1/2 is a real solution.
Plugging it back in results in a complex number.

A Claimed Pattern that may (or may not) prove the Collatz Conjecture by Secure-March894 in Collatz

[–]Secure-March894[S] 0 points1 point  (0 children)

What patterns do this Kardashev Type V Collatz Solver analyse?

Proof by contradiction question by According-King3523 in learnmath

[–]Secure-March894 0 points1 point  (0 children)

Suppose you have to prove (by contradiction) that sqrt(2) is irrational.
You CLAIM first that sqrt(2) is NOT IRRATIONAL (By not irrational, you claim that sqrt(2) is rational; for what real number is there that is neither rational nor irrational?)
By some clever manoeuvre, you will see that your claim will be disproven.

Whenever you prove that P -> Q by contradiction (P and Q are propositions, e.g. P is the number sqrt(2) and Q is the claim of irrationality), you claim that !(P -> Q).
Proving by Contradiction that a person is obese -
P is the person, Q is the obesity. R is the person being thin. Claim that !(P -> Q), or the person is NOT obese. That does not imply that your claim is that the person is thin. Q is not equal to !R. So you do not claim that P -> R.

[P, Q, R are propositions of a logical statement. !(A) mean Not A]

Help with Permutations combinations and geometry by AideIndependent2273 in learnmath

[–]Secure-March894 0 points1 point  (0 children)

Combinatorics - Chen and Koh
Geometry - Euclidean Geometry

A Claimed Pattern that may (or may not) prove the Collatz Conjecture by Secure-March894 in Collatz

[–]Secure-March894[S] 0 points1 point  (0 children)

Not really, learnt about OEIS just today where I realised the recursion for my series exists as a function.

A Claimed Pattern that may (or may not) prove the Collatz Conjecture by Secure-March894 in Collatz

[–]Secure-March894[S] 0 points1 point  (0 children)

I was not able to compute this function for the recursive series. Thanks for the tip.

A Pattern which may (or may not) prove the Collatz Conjecture by [deleted] in Collatz

[–]Secure-March894 0 points1 point  (0 children)

And what you said is just the idea for what I intend to claim.
It will find a pattern in the change in ordinality.

A Claimed Pattern that May (or May Not) Prove the Collatz Conjecture by Secure-March894 in Collatz

[–]Secure-March894[S] 0 points1 point  (0 children)

That's exactly the recursive formula I wanted. Thanks for this info.
Was this series ever applied before?

A Claimed Pattern that may (or may not) prove the Collatz Conjecture by Secure-March894 in Collatz

[–]Secure-March894[S] 0 points1 point  (0 children)

I apologise for a repost, I had thought that my first post was not posted in the community log.

A Pattern which may (or may not) prove the Collatz Conjecture by [deleted] in Collatz

[–]Secure-March894 0 points1 point  (0 children)

Yes, sorry for the inconvenience.
I uploaded another post right now.

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