How to "show" something in math

[Belegost]

Is there a reason they could not equal 0?

 

[Pretender]

also good to note that a, b, c, can't be -1

 

[Belegost]

The problem states that the variables are nonnegative numbers, which means they are equal to or greater then zero. However, in my proof I can see no reason the numbers cannot equal zero.

 

[thEnEuRoMancER]

a <= (b+c)

a/(1+a) <= ((b/(1+b)) + (c/(1+c)))

transform this to:

1/(1+1/a) <= (1/(1+1/b) + 1/(1+1/c))

multiply both sides with (1+1/a)*(1+1/b)*(1+1/c) to get

(1+1/b)*(1+1/c) <= (1+1/a)*(1+1/c) + (1+1/a)*(1+1/b)

1 + 1/b + 1/c + 1/(bc) <= 1 + 1/a + 1/c + 1/(ac) + 1 + 1/a + 1/b + 1/(ab)

1/(bc) <= 1 + 2/a + 1/(ac) + 1/(ab)

multiply both sides with abc to get

a <= abc + 2bc + b + c

now a <= b+c , so if we add abc + 2bc to the right side of inequality it will still hold

 

[Degenerate]

rightttt...... i cant get it. perhaps need more time...

 

[aolj]

If I'm not wrong, you could show the solution by induction method.
Thing is it's raining here and I've got to go. Hopefully, I can show it soon.

later.

 

[serialb]

Just wonder what class is GoldenBear in? Assuming you are a computer science junior, you should have taken discrete math. As aolj stated, mathematical induction will solve the problem in a simple and logical way. Go do a little search in google and I bet you will find some information on MI.