Let α be a root of the equation 1 + x 2 + x 4 = 0 . Then the value of α 1011 + α 2022 - &#945…

Let α be a root of the equation 1+x2+x4=0. Then the value of α1011+α2022-α3033 is equal to:
  1. 1
  2. α
  3. 1+α
  4. 1+2α

Solution

Given, x4+x2+1=0

Using the formula a4+a2+1=a2+a+1a2-a+1

We get, x2+x+1x2-x+1=0

⇒x=±ω, ±ω2 where ω=11/3 and imaginary.

So α1011+α2022-α3033=1+1-1=1

Asked in: JEE Main 2022 (29 Jun Shift 2)

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