## Solution The problem of this contest was to solve a polynomial: `x⁴ + 8x³ + 24x² + 32x + 15 = 0` This might look pretty hard, but if you know what to look for you might notice a regularity there. First of all you need to add 1: `x⁴ + 8x³ + 24x² + 32x + 16 = 1` And now the magic happens when you remove the factors typical for to the binomial theorem: `x⁴ + 4*2x³ + 6*4x² + 4*8x + 16 = 1` `x⁴ + 4*2¹x³ + 6*2²x² + 4*2³x + 2⁴ = 1` According to the binomial theorem that is equal to: `(x+2)⁴ = 1` taking the 4th root leads to the four solutions: `x₁+2 = 1 → x₁ = -1`, `x₂+2 = -1 → x₂ = -3`, `x₃+2 = i → x₃ = i-2`, `x₄+2 = -i → x₄ = -i-2` *↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓* ### List of participants with their entries: Name | solution found | comment - | - | - @crokkon | correct | @zuerich | correct | *↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓* ## Winner draw: Not necessary since the reward can be divided be the number of entries: Congratulations @zuerich and @crokkon , you won 1 SBI each! *↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓* ### The next contest starts in 2 days. Don't miss it!
author | quantumdeveloper |
---|---|
permlink | math-contest-23-results-and-solution |
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author | crokkon |
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woah this way to solve it is relly cool. Math impresses me every time I learn something new
author | kaeserotor |
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Hello, Your post has been manually curated by a @stem.curate curator. <center></Center><center> *Supporting Steemians on STEMGeeks*</center> We are dedicated to supporting great content, like yours on the [STEMGeeks](stemgeeks.net) tribe. Please join us on [discord](https://discord.gg/73WaANa).
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