Math Is Fun Forum

Liuz

Member

From: Himalayas

Registered: 2025-08-04

Posts: 38

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Proof of inequality

How to prove the arithmetic square root of ab<(b-a)/(lnb-lna)<(a+b)/2
(b>a>0)

Last edited by Liuz (2025-08-07 21:41:31)

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实迷途其未远，觉今是而昨非。                                                                  I did get lost. Maybe I haven't gone too far. Now I have come to realize how wrong I have been all those years.

Liuz

Member

From: Himalayas

Registered: 2025-08-04

Posts: 38

Website

Re: Proof of inequality

Anyone  can help me?

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实迷途其未远，觉今是而昨非。                                                                  I did get lost. Maybe I haven't gone too far. Now I have come to realize how wrong I have been all those years.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 51,413

Re: Proof of inequality

Be patient. Your question will be answered.

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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.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 294

Re: Proof of inequality

lnb? lna?

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Liuz

Member

From: Himalayas

Registered: 2025-08-04

Posts: 38

Website

Re: Proof of inequality

lna: the Napierian logarithm of a (also the natural logarithm of a)

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实迷途其未远，觉今是而昨非。                                                                  I did get lost. Maybe I haven't gone too far. Now I have come to realize how wrong I have been all those years.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 294

Re: Proof of inequality

I see, thank you. I usually write it as ln(a).

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

hypsin_0

Member

From: Earth

Registered: 2025-07-05

Posts: 71

Website

Re: Proof of inequality

Deepseek R1:
let t=b/a＞1
so

   

   

let

And !@#$%^&*()
then we got f(t)＞0 for t＞1
Tada!We proof the left part!

Last edited by hypsin_0 (2025-08-11 23:40:28)

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我死故我在。 I die,therefore I am.

hypsin_0

Member

From: Earth

Registered: 2025-07-05

Posts: 71

Website

Re: Proof of inequality

so Liuz,why don't you ask deepseek?

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我死故我在。 I die,therefore I am.

Liuz

Member

From: Himalayas

Registered: 2025-08-04

Posts: 38

Website

Re: Proof of inequality

My outdated phone is unable to do that. Anyway,it's more helpful to sharpen my mind through thinking and exchanging solutions.

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实迷途其未远，觉今是而昨非。                                                                  I did get lost. Maybe I haven't gone too far. Now I have come to realize how wrong I have been all those years.