A,b,c are given:

MathematicalPhysicist

Gold Member
and a+b+c>0 and abc>0
proove that abc>=a+b+c

bogdan

I'm afraid it's not correct...
if a=0.1,b=0.1,c=0.1 then abc=0.001 and a+b+c=0.3, 0.001<0.3...
[?]

MathematicalPhysicist

Gold Member
****, damn.
btw, bogdan, did these numbers were the first to pop up your head?

Last edited:

STAii

It is not really hard to get those numbers.
All you need to know is think for a moment ..
If you have a positive number (call it X), and you multiply it but another positive number (say Y), you can get one of the following results :
XY > X
XY < X
XY = X
Now, if XY = X then Y = 1, obviously this is the changing point between XY > X and XY < X
Try numbers bigger than 1 for Y, say, Y = 2, then XY = 2X, therefore XY > X (remember that X is positive).
Now, try numbers smaller than 1 (and more than 0, remember Y is positive), say, Y = 0.1, then you get XY = X/10, and therefore XY < X
bogdan was trying to disproove the original inequality, logically if he gets a sinlge case that gives a wrong answer in the inquality, then the inquality is wrong.
The inequality says that abc will be bigger or equal to a+b+c,
So, to disproove this try to get smaller value of abc than expected (since this MIGHT turn the inequality wrong, by making left side smaller).
Since values smaller than 1 for a,b,c will make abc smaller and smaller, bogdan have chosen 0.1 for all of them.
I see infinite number of cases that proove the inequality wrong.
Try those :
1- a=0.01, b=0.1, c=0.1
2- a=1, b=1, c=1
3- a=1.1, b=0.0001, c=0.0002

I wonder if maybe this was supposed to be in the domain of all the positive integers?

MathematicalPhysicist

Gold Member
I wonder if maybe this was supposed to be in the domain of all the positive integers?
let's say it is, does it change the answer?

bogdan

Yes...for positive integers it is true...
let's say 2<=a<=b<=c...it doesn't "particularize"...
we have abc>=2*(bc)>=4*c=c+c+c+c>a+b+c...

MathematicalPhysicist

Gold Member
do you have proof or what you have shown was your proof?

bogdan

That's the proof...read it carefuly... (that's not true for integers equal to 1...in specific cases...)

MathematicalPhysicist

Gold Member
Originally posted by bogdan
That's the proof...read it carefuly... (that's not true for integers equal to 1...in specific cases...)
thanks.

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