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3 + abcd >= a + b + c + d
can_hang2007   4
N Jan 26, 2021 by mihaig
Source: dedicated to ductrung...
Let $ a,b,c,d$ be nonnegative real numbers such that $ a^2 + b^2 + c^2 + d^2 = 3.$ Prove that
$ 3 + abcd \ge a + b + c + d.$
:)
4 replies
can_hang2007
Mar 25, 2009
mihaig
Jan 26, 2021
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3 + abcd >= a + b + c + d
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can_hang2007
2948 posts
can_hang2007
#1 h  Mar 25, 2009, 11:43 AM • 3 Y
Y by xyzz, Adventure10, Mango247
Let $ a,b,c,d$ be nonnegative real numbers such that $ a^2 + b^2 + c^2 + d^2 = 3.$ Prove that
$ 3 + abcd \ge a + b + c + d.$
:)
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sqing
41457 posts
sqing
#2 h  Jan 18, 2021, 7:49 AM
Y by
can_hang2007 wrote:
Let $ a,b,c,d$ be nonnegative real numbers such that $ a^2 + b^2 + c^2 + d^2 = 3.$ Prove that
$ 3 + abcd \ge a + b + c + d.$
:)
Good.
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mihaig
7339 posts
mihaig
#3 h  Jan 18, 2021, 8:51 AM
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A splendid and very instructive comment. Especially since you, along I and another colleague from China are the authors of the generalization of this problem. So the point of this "bump" is known by you only.
Good.
See the problem 494 from https://ssmr.ro/gazeta/gma/2019/gma1-2-2019-continut.pdf
This post has been edited 1 time. Last edited by mihaig, Jan 18, 2021, 9:03 AM
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Quantum_fluctuations
1282 posts
Quantum_fluctuations
#5 h  Jan 26, 2021, 6:17 AM
Y by
mihaig wrote:
A splendid and very instructive comment. Especially since you, along I and another colleague from China are the authors of the generalization of this problem. So the point of this "bump" is known by you only.
Good.
See the problem 494 from https://ssmr.ro/gazeta/gma/2019/gma1-2-2019-continut.pdf

If I am not violating any policy of AOPS, I would like to ask...Is he a professor? Is his surname sqing and has he written any books or articles?
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mihaig
7339 posts
mihaig
#6 h  Jan 26, 2021, 6:29 AM
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Quantum_fluctuations wrote:
If I am not violating any policy of AOPS, I would like to ask...Is he a professor? Is his surname sqing and has he written any books or articles?

I'm afraid I don't even know how to start a proof to your proposed problems.
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