Math Is Fun Forum

devkumararora

Member

Registered: 2011-06-09

Posts: 11

Interesting question MIND FREAKING

Whick of the following is equal

?
A)

B)

C)

C)

MathPro101

Member

Registered: 2011-06-08

Posts: 18

Re: Interesting question MIND FREAKING

When you set them all equal to each other, {A}^{1/A}={B}^{1/B}={C}^{1/C}, can you not conclude that A=B=C?

Last edited by MathPro101 (2011-06-09 05:50:17)

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Interesting question MIND FREAKING

Hi,

I'm getting:

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

RauLiTo

Member

From: Bahrain

Registered: 2006-01-11

Posts: 142

Re: Interesting question MIND FREAKING

9 ^ Abc

---

ImPo$$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Interesting question MIND FREAKING

We can also have:

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

devkumararora

Member

Registered: 2011-06-09

Posts: 11

Re: Interesting question MIND FREAKING

also the method

devkumararora

Member

Registered: 2011-06-09

Posts: 11

Re: Interesting question MIND FREAKING

Hi,

I'm getting:

what is the method used

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Interesting question MIND FREAKING

Hi,

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

devkumararora

Member

Registered: 2011-06-09

Posts: 11

Re: Interesting question MIND FREAKING

dear  gAr,
you have taken k as A^1/A ,B^1/B, C^1/C
then how can you write it as  k^ABC+ k^ABC+ k^ABC ???
please explain

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Interesting question MIND FREAKING

hi dev

i'm getting the same as gAr

Last edited by anonimnystefy (2011-06-10 05:16:38)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Interesting question MIND FREAKING

hi

I agree with gAr's analysis.  But do A, B and C exist (in real numbers let's say) ?

so

so I plotted the graph of y = logx and the graph of y = x.logk, using 'x' to replace 'A' and trying various values for logk

see graph below.

Either the line fails to hit the curve at all; or it touches as a tangent once; or it crosses twice (which I show with logk = 0.11)

But we also want B and C to have this property so I think this means that if k, A, B and C exist in reals then either

(i) A = B = C

or

(ii) at least a pair are equal, let's say wnlog, B = C

That's it for the moment I'm afraid. 

Bob

Last edited by Bob (2011-06-10 06:07:24)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

devkumararora

Member

Registered: 2011-06-09

Posts: 11

Re: Interesting question MIND FREAKING

hi

I agree with gAr's analysis.  But do A, B and C exist (in real numbers let's say) ?

so

so I plotted the graph of y = logx and the graph of y = x.logk, using 'x' to replace 'A' and trying various values for logk

see graph below.

Either the line fails to hit the curve at all; or it touches as a tangent once; or it crosses twice (which I show with logk = 0.11)

But we also want B and C to have this property so I think this means that if k, A, B and C exist in reals then either

(i) A = B = C

or

(ii) at least a pair are equal, let's say wnlog, B = C

That's it for the moment I'm afraid. 

Bob

All are wrong ANSWERs
answer is  B) {2}^{1/2}

devkumararora

Member

Registered: 2011-06-09

Posts: 11

Re: Interesting question MIND FREAKING

We can also have:

All are wrong ANSWERs
answer is  B) {2}^{1/2}

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Interesting question MIND FREAKING

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Interesting question MIND FREAKING

hi gAr

Are you saying that there's a multiplicity of possible values for A, B, C and k?  I didn't think we had any yet;  in the sense that: we're asked to pick from (a), (b), (c) or (d).

Bob

Last edited by Bob (2011-06-11 01:56:30)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Interesting question MIND FREAKING

Hi Bob,

It's not possible to have real solution if A, B and C are all distinct. But the question mentions nothing about A, B and C!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Interesting question MIND FREAKING

hi devkumararora

In post #12 you say

All are wrong ANSWERs
answer is  B) {2}^{1/2}

I wasn't offering my analysis as an 'answer'; just a step on the way to an answer (maybe).  Are you saying I've made a mathematical mistake ? (entirely possible; I make them all the time; but I need to know what mistake).

Meanwhile you say (b),  root 2,  is the answer.

Have you some working to support this because I'd like to see it; or just that you have the 'official' answer?

RauLiTo :  You offer 9^ABC but again, may I see your working for this?

gAr: Ok it doesn't ask us to state values for A, B, and C ... but I'd rather like to know if values exist.  It would be a very curious problem if it were possible to answer the multi-choice, and yet, no actual values for the letters exist.  That is, for me, an even harder concept.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Interesting question MIND FREAKING

Hi Bob,

By symmetry, we must have A^(BC) = B^(AC) = C^(AB) = 243.
And I chose, A^(1/A) = B^(1/B) = C^(1/C) = 243, hoping that there may be many complex solutions for x^(1/x) = 243.

I entered x^(1/x) = 243 into wolframalpha, it answered in terms of ProductLog function.
Don't have anything neat yet!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Interesting question MIND FREAKING

hi gAr

I thought I'd try each multi-choice answer and see what values pop out.

But, it's beginning to look like A, B, C  will end up complex for all four.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Interesting question MIND FREAKING

Hi Bob,

Yes, I too think so.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Interesting question MIND FREAKING

hi gAr

Using

Consider the graph

So when does

have

as a tangent?

using (1)

see graph

So for real values of A, B, C

when

(a)

when

(c)

when

(d)

when

(b)

So for all four answers k is too big for any real solutions for A, B, and C.

Bob

Last edited by Bob (2011-06-11 21:05:55)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Interesting question MIND FREAKING

Hi Bob,

Thanks for the explanation!
Yes, there can be no real solutions.

I'm unable to find even a complex solution. That k also might be a complex number.
Or is there any solution at all?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

devkumararora

Member

Registered: 2011-06-09

Posts: 11

Re: Interesting question MIND FREAKING

No need to worry my friends
i got the question from one of my books
at back the answer was {2}^{1/2}
I THINK THE QUESTION IS WRONG I THINK IT SHOULD BE

devkumararora

Member

Registered: 2011-06-09

Posts: 11

Re: Interesting question MIND FREAKING

I Am Having Doubts I A Bunch Of Questions Would You All Solve Them For Me Please

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Interesting question MIND FREAKING

sure

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.