Question

if α and β are zeros of x^2+x+1 then find values of 1/α + 1/β and α^2+β^2 ???

Answer 1

α and β are zeroes of x²+x+1=0.
then,
α+β=-b/a
      = -1
αβ=c/a
    =1
1/α+1/β=(α+β)/αβ
            = -1/1
            = -1
(α+β)² = α²+β²+2αβ
⇒(-1)²=α²+β²+2×1
⇒1-2=α²+β²
⇒α²+β² = -1