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Math Contest #23 Results and Solution by quantumdeveloper

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· @quantumdeveloper ·
$0.39
Math Contest #23 Results and Solution
## 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!
👍  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
👎  
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@crokkon · (edited)
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@kaeserotor ·
woah this way to solve it is relly cool. Math impresses me every time I learn something new
👍  
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@stem.curate ·
Hello,

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