Math, asked by priya25051, 6 hours ago

x²+x+1= 0 then x²⁰¹⁸+x²⁰¹⁹ is?

Answers

Answered by vyaswanth
0

Step-by-step explanation:

here omega and omega square are roots

here w indicates omega

1 + w +  {w}^{2}  = 0

satisfies this equation

this is also known as cubeth roots of unity

conditions for these are

1 + w +  {w}^{2}  = 0 \\ w^{3}  = 1

here the given equation satisfies for cubeth root of unity

x = w \\ x =  {w}^{2}

now substituting them gives

 {x}^{2018}  + {x}^{2019}  \\  {(w)}^{2018}  + (w)^{2019}  \\  =  > 1 + w^{2}

 =  >  - w =  \frac{1 +  \sqrt{3}i }{2}

here is the answer

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