Given that , prove that .

Attempted solution:

....

Where do I go from here?

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- May 20th 2012, 10:57 AMRogueDemonDifficult Proof
Given that , prove that .

Attempted solution:

....

Where do I go from here? - May 20th 2012, 11:46 AMemakarovRe: Difficult Proof
- May 22nd 2012, 01:23 PMRogueDemonRe: Difficult Proof
Would the conclusion be true if (D - B) and (C - A) were absolute values? If so, would it be possible to prove this?

- May 22nd 2012, 03:58 PMemakarovRe: Difficult Proof
Interesting. Yes, if AB = CD and neither A = C = 0 nor B = D = 0, then . Under these assumptions, B = 0 iff C = 0 and A = 0 iff D = 0. Check what happens when B = 0 and C = 0, or when A = 0 and D = 0. The remaining case is when neither of the numbers equals 0. Then AB = CD implies A / C = D / B. Let's call this number x. We have

iff

iff

iff

which is true.