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Given that x, y, and z are all real numbers, find the minimum possible value of . I don't know how to tackle these kinds of problems. Thanks. —Preceding unsigned comment added by 70.111.95.226 ( talk) 03:18, 14 April 2008 (UTC)
The function f(x,y,z)= x4+y4+z4−4xyz is symmetrical. (f(x,y,z)=f(z,y,x)=f(y,x,z)=&c). f(x,x,x)=3x4−4x3 has minimum f(1,1,1)=−1. Is that a local minimum for f(x,y,z)? Are there other local minima? Bo Jacoby ( talk) 12:34, 14 April 2008 (UTC).
Also, you can use the AM-GM inequality applied to x^4, y^4, z^4 and 1^4.
(x^4 + y^4 + z^4 + 1^4)/4 ≥ xyz
therefore
x^4 + y^4 + z^4 + 1 ≥ 4xyz
x^4 + y^4 + z^4 - 4xyz ≥ -1
so you can get the minimum without finding the actual values of x,y and z. 91.143.188.103 ( talk) 21:33, 14 April 2008 (UTC)
for quite some time the mathematicians have thought the mean value conditions is quite enough for afunction to be continouse at acertain point until RIEMANN gave his abs(x),where it satisfies the mean value at zero but not continouse at zero.my question is that i recall afunction but i cannot find it,it satisfies the mean value at every pints within it`s range but it is not continouse at all of those points.any one can tell me what is that function?thank you very much. Husseinshimaljasimdini ( talk) 09:26, 14 April 2008 (UTC)
I've just about convinced myself that the following problem has no feasible solution - can someone either confirm this, or find one?
Four people who walk at the same speed are to complete a certain route. There is available one bicycle and one moped, each of which can carry only one person. Each person will ride the bicycle at the same speed and the moped at the same speed. Suppose that walk/bicycle/moped speeds are 5/10/20 mph. It is required that all four people start and end the journey together - this is to be achieved by each walking half the distance, riding the bicycle for one quarter of the distance and riding the moped for one quarter of the distance. These fractions can be made up of any number of smaller components.
Everything I've tried breaks down by the bicycle being required somewhere before it has arrived.— 81.132.237.15 ( talk) 18:29, 14 April 2008 (UTC)
In 1996 Torsten Jensen was awarded the Millennium Leibniz Prize in logic, mathematics, physics, chemistry and medicine by providing a beautifully crafted very short proof that showed that all natural numbers can be divided by 3 and therefore Euclides theorem is false, invalid and worthless.
My question is this: 1. Do you know his ultra simple proof? 2. Why Euclides himself did not think of it? 3. Why did it take about 2300 years before a man saw the error in Euclid's theorem and destroyed about 12,000 rubbish theorems in number theory including Andrew Wiles's attempt at finding a proof for Fermat's last theorem?
Signed: T. Hansen, Lans, German Lutheran Church <email removed>
I do not mind at all if people read and steal my thoughts. —Preceding unsigned comment added by 81.152.51.207 ( talk) 20:51, 14 April 2008 (UTC)
Sure, all natural numbers can be divided by 3, but you don't get a natural number at the end of it 67% of the time. What's your point? -- Tango ( talk) 22:44, 14 April 2008 (UTC)
Mathematics desk | ||
---|---|---|
< April 13 | << Mar | April | May >> | April 15 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Given that x, y, and z are all real numbers, find the minimum possible value of . I don't know how to tackle these kinds of problems. Thanks. —Preceding unsigned comment added by 70.111.95.226 ( talk) 03:18, 14 April 2008 (UTC)
The function f(x,y,z)= x4+y4+z4−4xyz is symmetrical. (f(x,y,z)=f(z,y,x)=f(y,x,z)=&c). f(x,x,x)=3x4−4x3 has minimum f(1,1,1)=−1. Is that a local minimum for f(x,y,z)? Are there other local minima? Bo Jacoby ( talk) 12:34, 14 April 2008 (UTC).
Also, you can use the AM-GM inequality applied to x^4, y^4, z^4 and 1^4.
(x^4 + y^4 + z^4 + 1^4)/4 ≥ xyz
therefore
x^4 + y^4 + z^4 + 1 ≥ 4xyz
x^4 + y^4 + z^4 - 4xyz ≥ -1
so you can get the minimum without finding the actual values of x,y and z. 91.143.188.103 ( talk) 21:33, 14 April 2008 (UTC)
for quite some time the mathematicians have thought the mean value conditions is quite enough for afunction to be continouse at acertain point until RIEMANN gave his abs(x),where it satisfies the mean value at zero but not continouse at zero.my question is that i recall afunction but i cannot find it,it satisfies the mean value at every pints within it`s range but it is not continouse at all of those points.any one can tell me what is that function?thank you very much. Husseinshimaljasimdini ( talk) 09:26, 14 April 2008 (UTC)
I've just about convinced myself that the following problem has no feasible solution - can someone either confirm this, or find one?
Four people who walk at the same speed are to complete a certain route. There is available one bicycle and one moped, each of which can carry only one person. Each person will ride the bicycle at the same speed and the moped at the same speed. Suppose that walk/bicycle/moped speeds are 5/10/20 mph. It is required that all four people start and end the journey together - this is to be achieved by each walking half the distance, riding the bicycle for one quarter of the distance and riding the moped for one quarter of the distance. These fractions can be made up of any number of smaller components.
Everything I've tried breaks down by the bicycle being required somewhere before it has arrived.— 81.132.237.15 ( talk) 18:29, 14 April 2008 (UTC)
In 1996 Torsten Jensen was awarded the Millennium Leibniz Prize in logic, mathematics, physics, chemistry and medicine by providing a beautifully crafted very short proof that showed that all natural numbers can be divided by 3 and therefore Euclides theorem is false, invalid and worthless.
My question is this: 1. Do you know his ultra simple proof? 2. Why Euclides himself did not think of it? 3. Why did it take about 2300 years before a man saw the error in Euclid's theorem and destroyed about 12,000 rubbish theorems in number theory including Andrew Wiles's attempt at finding a proof for Fermat's last theorem?
Signed: T. Hansen, Lans, German Lutheran Church <email removed>
I do not mind at all if people read and steal my thoughts. —Preceding unsigned comment added by 81.152.51.207 ( talk) 20:51, 14 April 2008 (UTC)
Sure, all natural numbers can be divided by 3, but you don't get a natural number at the end of it 67% of the time. What's your point? -- Tango ( talk) 22:44, 14 April 2008 (UTC)