Math Olympiad Problem - USA
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- เผยแพร่เมื่อ 13 พ.ค. 2024
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Meanwhile I used x=0 as a first try
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!
@@wauchi1895 its a math olympiad problem because you need to prove why there aren't any other solutions
@@owen549 Why though?
What's important is the solution and how you've got to it (to make sure you didn't cheat).
@@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
@@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
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.
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?
That's math
Well explained
Glad it was helpful
So its
1+1-1+1-1=1
yes