elegant problem 3 (1 Viewer)

[OLDMAN]

a,b both positive and a+b < ab. Prove a+b > 4.

 

[underthesun]

I don't quite understand the problem. Is this a complex number question?

 

[ND]

I don't get it either.

 

[Affinity]

The question was a,b are positive and ab > a+b, prove a+b > 4
surely it was posted 'elegantly'

(sqrt(a)-sqrt(b))^2 >= 0

....

sqrt(a+b) > 2

....

 

[ND]

Originally posted by Affinity
The question was a,b are positive and ab > a+b, prove a+b > 4

Do you read minds? Or am i missing something?

edit: nevermind, got it now.

 

[Affinity]

by the way how do you escape key characters? is it a slash or something?

 

[Archman]

let a+b = n
n>=2sqrt(ab)
n^2/4>=ab
n^2/4>n
n>4 (n obv cant be 0)

 

[turtle_2468]

affinity = good

 

[OLDMAN]

what can I say? How did Affinity decipher this Q, and proceed to solve it.

What went wrong with my typing? Typed it twice, edit it once.

Just to test whether it does it again :
a,b both positive and a+b < ab. Prove a+b > 4.

 

[BlackJack]

Ah... the problem is, never use the less than sign followed by the greater than sign because the computer thinks it's a HTML tag.
e.g. x² uses the superscript tag

That, or turn HTML coding off when you create the thread.

The easy way to find out is: edit.

edit: or quote...

 

[OLDMAN]

Thanks Blackjack.

 

[McLake]

OK, I fixed your posts OLDMAN.

The HTML code is like this (but replace "a" with "&"):

alt; - less than
agt; - greater than

 

[OLDMAN]

Thanks McLake. <

 

[OLDMAN]

btw, nice soln, Archman.

 

[Affinity]

by the way, can we assume AM-GM

 

[underthesun]

im a bit stupid, so what's AM-GM?

 

[flyin']

Arithmetic Mean and Geometric Mean?

 

[OLDMAN]

Usually asked as part i) prove a+b>sqrt(ab) etc.