Find x^5 !!!
If x 4 + x 3 + x 2 + x + 1 = 0 , what is the value of x 5 ?
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2 solutions
Using the idea of roots of unity to get the equation x 5 − 1 = ( x − 1 ) ( x 4 + x 3 + x 2 + x + 1 ) and substituting 0 into the equation gives x 5 − 1 = 0 x 5 = 1
But the equation is x 4 + x 3 + x 3 + x 2 + 1 D:
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I have been fooled :O I must be drunk, oh well using Brilliant pass midnight might be a bad idea. Should I delete the solution?
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Maybe you should, but I couldn't find any solution there.
if
x 5 = 1
then, x = 1
use 1 in the problem you'll be surprised.
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@Pratyya Ghosh – Yes, actually I though it was a typo but then I found the missing x again! Very busy so I can't try it D:
@Pratyya Ghosh – That claim is not true x 5 = 1 ⇒ x = 1 .
Though yes, we have x = 1 ⇒ x 5 = 1 .
Thanks, I have updated the problem statement.
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Have a problem with this problem. The 4 roots of this equation are all complex numbers and if we make one of it to power 5 we get other complex number different from 1. So x^5 is not 1.
On multiplying the equation with x we get, x 5 + x 4 + x 3 + x 2 + x = 0 Subtracting this equation with the original one gives x 5 − 1 = 0 Therefore, x 5 = 1