Math Is Fun Forum

engrymbiff

Member

Registered: 2010-06-14

Posts: 30

Show that (413)^(1/3)>6+3^(1/3)

How to do this?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Show that (413)^(1/3)>6+3^(1/3)

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.

engrymbiff

Member

Registered: 2010-06-14

Posts: 30

Re: Show that (413)^(1/3)>6+3^(1/3)

Sorry, that didn't help me..

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Show that (413)^(1/3)>6+3^(1/3)

Hi Bobbym,
Is it okay to start with the thing we are trying to prove?

---

'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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Show that (413)^(1/3)>6+3^(1/3)

Hi;

This is the problem:

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Show that (413)^(1/3)>6+3^(1/3)

Hi bobbym

I think what Agnishom wanted to ask you is whether it is okay to start the proof with what we want to prove and work our way to a true statement...

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Show that (413)^(1/3)>6+3^(1/3)

Hi anonimnystefy;

I missed that. I am sorry about that. Bob and I had a good discussion on that and it seems better to work backwards in that case. Even though they do work forwards a lot in inequality books.

Unfortunately, whatever brilliant idea I had  about this problem 1 year ago, I can not remember it at all.

---

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.

engrymbiff

Member

Registered: 2010-06-14

Posts: 30

Re: Show that (413)^(1/3)>6+3^(1/3)

Hm... I really cannot solve it, I have a vague memory of how I solved it last time but now I don't have a good clue of how...

scientia

Member

Registered: 2009-11-13

Posts: 224

Re: Show that (413)^(1/3)>6+3^(1/3)

I have a very weird solution; you probably won't like it but I'll have a go anyway.

Let

.

Then

because

.

Let

.

We find

(just). It follows that

since the quadratic function is strictly increasing for positive x.

The LHS is

and so we are done.