# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #351 2006-01-07 23:18:08

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Problems and Solutions

x^2+y^2=x^2+y^2+2xy-2xy=(x+y)^2-2xy=1-2xy.
x^4+y^4=17=x^2^2+y^2^2+2x^2y^2-2x^2y^2=(x^2+y^2)^2-2x^2y^2=(1-2xy)^2-2x^2y^2 = 1-4xy+4x^2y^2-2x^2y^2=1-4xy+2x^2y^2 =>
2x^2y^2-4xy=17-1=16
x^2y^2-2xy=16/2=8

IPBLE:  Increasing Performance By Lowering Expectations.

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## #352 2006-01-08 04:51:53

irspow
Member
Registered: 2005-11-24
Posts: 1,055

### Re: Problems and Solutions

I might be missing something obvious, but...

1/2 + 1/3 + 1/4 = 13/12?  Doesn't one of the partners in k+78 own a 1/12 imaginary share?

I think that this problem could only be solved if we knew who was holding the fake share.

Last edited by irspow (2006-01-08 04:54:55)

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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## #353 2006-01-08 16:22:43

Jai Ganesh
Registered: 2005-06-28
Posts: 47,365

### Re: Problems and Solutions

krassi_holmz is right!
To irspow : In problem # k + 78, when it is stated that the shares are in the ration a:b:c, it need not be true that a+b+c be equal to 1. a's share of the total would be a/(a+b+c), b's share would be b/(a+b+c) and c's c/(a+b+c).

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #354 2006-01-08 17:28:19

Jai Ganesh
Registered: 2005-06-28
Posts: 47,365

### Re: Problems and Solutions

Problem # k + 83

Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. What is the area left ungrazed by the horses?

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #355 2006-01-08 17:45:49

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Problems and Solutions

70^2 - 45^2 Pi ?

IPBLE:  Increasing Performance By Lowering Expectations.

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## #356 2006-01-08 22:50:51

Jai Ganesh
Registered: 2005-06-28
Posts: 47,365

### Re: Problems and Solutions

krassi_holmz, you are given another chance.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #357 2006-01-09 03:36:33

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Problems and Solutions

Last edited by Ricky (2006-01-09 03:40:26)

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #358 2006-01-09 13:06:26

irspow
Member
Registered: 2005-11-24
Posts: 1,055

### Re: Problems and Solutions

Last edited by irspow (2006-01-09 13:39:29)

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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## #359 2006-01-09 16:16:22

Jai Ganesh
Registered: 2005-06-28
Posts: 47,365

### Re: Problems and Solutions

Well done, irspow

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #360 2006-01-09 16:39:06

Jai Ganesh
Registered: 2005-06-28
Posts: 47,365

### Re: Problems and Solutions

Problem # k + 84

Two spheres of radii 6 cm and 1 cm are inscribed in a right circular cone. The bigger sphere touches the smaller sphere and also the base of the cone. What is the height of the cone?

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #361 2006-01-10 11:21:02

irspow
Member
Registered: 2005-11-24
Posts: 1,055

### Re: Problems and Solutions

I'll take an ill-attempted stab.

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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## #362 2006-01-10 21:54:50

Jai Ganesh
Registered: 2005-06-28
Posts: 47,365

### Re: Problems and Solutions

irspow is correct! Although the actual solution is arrived at differently!

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #363 2006-01-10 21:58:32

Jai Ganesh
Registered: 2005-06-28
Posts: 47,365

### Re: Problems and Solutions

Probelm # k + 85

If u and v are the roots of the equation x² + ax + b = 0, what are roots of the equation x² -ax + b = 0?

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #364 2006-01-11 03:02:37

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Problems and Solutions

That's an interesting one. I think it's something like this:

Why did the vector cross the road?
It wanted to be normal.

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## #365 2006-01-11 04:16:41

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Problems and Solutions

I'm not sure, this is what I get:

Last edited by Ricky (2006-01-11 04:16:58)

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #366 2006-01-11 05:09:16

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Problems and Solutions

I think our answers are the same, and I've just taken a long way round.

Why did the vector cross the road?
It wanted to be normal.

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## #367 2006-01-11 08:34:24

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Problems and Solutions

Yea, I guess they are.  They looked completely different at first glance.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #368 2006-01-11 11:32:20

irspow
Member
Registered: 2005-11-24
Posts: 1,055

### Re: Problems and Solutions

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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## #369 2006-01-14 03:44:50

irspow
Member
Registered: 2005-11-24
Posts: 1,055

### Re: Problems and Solutions

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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## #370 2006-01-14 06:33:56

irspow
Member
Registered: 2005-11-24
Posts: 1,055

### Re: Problems and Solutions

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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## #371 2006-01-14 08:12:05

irspow
Member
Registered: 2005-11-24
Posts: 1,055

### Re: Problems and Solutions

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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## #372 2006-01-14 12:15:28

irspow
Member
Registered: 2005-11-24
Posts: 1,055

### Re: Problems and Solutions

darn that k+42, I just cant figure it.  Please someone, put me out of my misery.  I think that you have to incorporate a geometric series somehow, but everything that I try turns to nonsense.

I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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## #373 2006-01-14 12:47:28

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Problems and Solutions

Yes, k+42 is an incredibly difficult one. I think it could probably be solved brutally by getting excel to do all the calculations for you, but it's still tough.

Also, I think your answer to k+40 is wrong. I remember it being much smaller.

Why did the vector cross the road?
It wanted to be normal.

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## #374 2006-01-14 16:12:47

ryos
Member
Registered: 2005-08-04
Posts: 394

### Re: Problems and Solutions

I didn't check if this one has already been solved, but since irspow asked about it, I gave it a go.

Last edited by ryos (2006-01-14 16:15:25)

El que pega primero pega dos veces.

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## #375 2006-01-14 17:13:17

Jai Ganesh
Registered: 2005-06-28
Posts: 47,365

### Re: Problems and Solutions

Four   days Pongal  break, and so  many solutions posted! I  shall reply to all of them after I return from Holiday on  Jan 16. mathsyperson is right, irspow's solution to problem # k + 40 isn't correct. It is much smaller. . Same about ryos' solution to problem # k + 42.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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