Math Olympiad Problem - USA

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[@aldoorymahagoub3951]

Meanwhile I used x=0 as a first try

[@wauchi1895]

Was literally going to type that. Not sure why it's a math olympiad problem, but perhaps my standards are pretty high. But yeah x=0 just makes everything 1. And because we have 3 positives, and 2 negatives. This is essentially 3-2=1. Tada!

[@owen549]

@@wauchi1895 its a math olympiad problem because you need to prove why there aren't any other solutions

[@wauchi1895]

@@owen549 Why though? What's important is the solution and how you've got to it (to make sure you didn't cheat).

[@owen549]

@@wauchi1895 thats just the way it is. complex equations can have multiple solutions whether it be complex or fractional randomly guessing on any math olympiad without showing steps and/or proving why thats the only solution means you dont get any points

[@wauchi1895]

@@owen549 What exactly is there to prove? x^0=1, that is consistent across variables, it's a rule for a reason. And from there our numbers don't actually matter, as all of them will be 1s anyways. Which lends us with 3 positives and 2 negatives, 3-2=1. Therefore our x=0 did work as the final result was the intended =1

[@spezinishizumi6099]

Its easier. Because every exponential function a^x is injective, the sum of them are injective. So the equation has only one solution. If you try, you get 0. Because the equation has only 1 Solution, you've found them all: L={0}. Done.

[@steveharry4678]

Well explained

[@zetutor]

Glad it was helpful

[@celestic6596]

How do you know how to go about separating the numbers like that, and also to multiply by 2, and only using the separated 2 sometimes?

[@zetutor]

That's math

[@duckyoutube6318]

So its 1+1-1+1-1=1

[@zetutor]

yes