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if z^2+z+1=0 then find the value of (z+1/z)^2 +(z^2+1/z^2)^2

if z^2+z+1=0 then find the value of (z+1/z)^2 +(z^2+1/z^2)^2
 

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Z² + z +1 = 0
Hence
Z is w or w²
Let z= w in the question
(w + 1/w)² + (w² +1/w²)²
= (w +w²)² + (w² + w) ²
= (-1)² + (-1)²
= 1 +1 
= 2

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