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## #1 2014-04-04 13:19:48

harrychess
Member
Registered: 2014-04-04
Posts: 33

Find all values of p such that 2(x+4)(x-2p) has a minimum value of -18.

How do you work this problem?

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## #2 2014-04-04 13:47:26

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2014-04-04 13:53:46

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
Website

Hi bobbym;

What does

``````p \[Element]
Reals && ((x < -4 && p <= (-9 + 4 x + x^2)/(8 + 2 x)) ||
x == -4 || (x > -4 && p >= (-9 + 4 x + x^2)/(8 + 2 x)))``````

mean?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #4 2014-04-04 13:55:27

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Check post #2. That code is incomplete.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2014-04-04 13:57:27

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
Website

How did you do that?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #6 2014-04-04 13:57:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

The experimental way of course.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #7 2014-04-04 14:02:36

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
Website

I hope you do not mean plugging in random numbers!

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #8 2014-04-04 14:04:03

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hahhahahahhaahhahahah! Oh Mr. Chattopadhyay you are in rare form today. Thank you, I needed to laugh and that was funny.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #9 2014-04-04 14:12:41

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

I am getting p=-5 with the p=1 bobbym got,

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## #10 2014-04-04 14:13:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #11 2014-04-04 14:14:24

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

Are you getting any other possibility?

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## #12 2014-04-04 14:17:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

I am looking for something else but so far no.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #13 2014-04-04 14:18:26

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

Agnishom wrote:

I hope you do not mean plugging in random numbers!

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## #14 2014-04-04 19:36:50

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
Website

``````In[1]:= 2 (x + 4) (x - 2 p)

Out[1]= 2 (4 + x) (-2 p + x)

In[2]:= \!\(
\*SubscriptBox[\(\[PartialD]\), \(x\)]\((2\ \((4 +
x)\)\ \((\(-2\)\ p + x)\))\)\)

Out[2]= 2 (4 + x) + 2 (-2 p + x)

In[3]:= Solve[% == 0, x]

Out[3]= {{x -> -2 + p}}

In[4]:= 2 (4 + x) (-2 p + x) /. {{x -> -2 + p}}

Out[4]= {2 (-2 - p) (2 + p)}

In[8]:= Solve[2 (-2 - p) (2 + p) == -18, p]

Out[8]= {{p -> -5}, {p -> 1}}``````

For harrychess:

Let f(x) = 2 (x + 4) (x - 2 p)
Let f'(x) be the derivative of f(x) with respect to x [,i.e, 2 (4 + x) + 2 (-2 p + x)]
Let g(p) be a polynomial in terms of p which satisfies the equation f'(x) = 0 [,i.e, x = p - 2]
Find p such that 2 (g(p) + 4) (g(p) - 2p) = -18 [,i.e, Solve this, 2 ( 4+ (p-2)) ((p-2)-2p)=-18]

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #15 2014-04-05 12:57:54

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,850
Website

Hi bobbym,

Is the above experimental enough?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #16 2014-04-05 13:33:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

I did it in a similar way but there is a shorter way to do the problem I think.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #17 2014-04-05 15:13:25

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

I found solutions for these:

p=-7
p=-5
p=1
p=3

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #18 2014-04-05 15:49:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi phrontister;

Did you test that in geogebra?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #19 2014-04-06 02:11:30

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

No, I didn't think of it.

So now I've entered the x and p coordinates into G and got the result as per image, but I don't know what to do next.

A straight-line connector isn't going to give any solutions, which I suppose means that I need to fit a curve, probably a separate one for ABC and DEF (I'm only guessing). However, I tried that and failed, except with 3-point circles through ABC and DEF...from which I don't get any other solutions either.

In fact, I think there are no non-integer solutions, and my spreadsheet seems to indicate that my integer solutions are the only answers to this puzzle.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #20 2014-04-06 03:17:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi phrontister;

There are only 2 answers for p.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #21 2014-04-06 04:07:43

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Hi Bobby,

I got 4 answers for p (ie, -7, -5, 1 and 3):

p = -7 and x = -13.....2(-13+4)(-13-2*-7) = -18
p = -7 and x = -5.......2(-5+4)(-5-2*-7) = -18
p = -5 and x = -7.......2(-7+4)(-7-2*-5) = -18
p = 1 and x = -1........2(-1+4)(-1-2*1) = -18
p = 3 and x = -3........2(-3+4)(-3-2*3) = -18
p = 3 and x = 5.........2(5+4)(5-2*3) = -18

Did I misunderstand something about the question, or make an error?

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #22 2014-04-06 04:12:49

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi;

You can check these quickly with geogebra.

When p = - 7 the minimum is - 50

When p = 3 the minimum is - 50

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #23 2014-04-06 04:25:08

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Oops! I overlooked the word 'minimum! >facepalm<

Yes...there are only solutions 1 and -5.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #24 2014-04-06 04:29:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Misheeru is the facepalm kid. I can not deal with two of ya. My brain is exploding.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #25 2014-04-06 04:38:27

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594