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What class are you taking; also, is it an online class? I cannot read the image. Can you take a focused picture of the relevant parts of the...

204.82 - 35.53 = 169.29 So they're treating this as YOU previously owed them 35.53. Tuff bananas :twisted:

If a,b & c>0, then: (a+b)/2 ≥√(ab) do the same for other pairs of numbers and multiply those together.

That's very interesting. It does indeed solve the equation (I used WolframAlpha to get the value of LambertW). It's interesting that such a...

Please state the Invariant Principle, as you were taught it, so we can help you apply it. I can't tell what it is from what you have said, or from a...

Hmmmm....is that not same as: (a + b)(a + c)(b + c) ≥ 8abc where a,b,c are integers > 0 ?

MarkFL deserves a round of applause for generating that demonstration. What a trooper! :)

(gol)F (IX) ED = in the bag : nice!!

CAB(taxi)BAG(catch)E(mbezzler) = CASH

NOTHING puzzles me...I simply have never seen a similar one! But then charades are charades, right?!

The NYT it is!!!

Try dividing both sides by ab, and see if you can make the inequality equivalent to one that is known to be true. Then you can reverse your steps to...

And, no, the answer is not MR COHEN :lol:

Oh for pete's sake. I started with the Doctor's 5-letter word and dropped the w on the floor at the same time. Double-arrgh!

Actually, a and b are not just "any value". The given inequality is not true, if either a or b is zero or negative. The point is not to prove...

You meant this, right? = - + - + - = + = - + - + - = + = - + - + - = + = - + - + - = - + - + - = + = - + - + - = + = - + - + - = + = - + - + - =...

Isn't this a trivial proof as (a-b)^{2} \geq 0 is true for any value of a or b?

What you've done so far is standard and correct (except for one sign error, if I'm right); it just left you at a point where (apart from factoring...

We are given so solve: \displaystyle \left(x^2-5x+5\right)^3=1 We could arrange this as a difference of cubes: \displaystyle...

Thanks, I solved it.

Heh. Didn't realize my proof was synthetic. Continuing from where Roger.Robert left off, I set the inequality to zero and factored the left-hand...

Of course, you can't, strictly speaking, prove a statement by assuming it is true! What you can do is start from the (a- b)^2= a^2- 2ab+...

That took 25 minutes, 'cuz I didn't cheat. (I was about to.) Clever. :) How did you discover that? = - + - + - = + = - + - + - = + = - + - + -...

Multiply each side by ab. Does that give you any ideas?