Let α and β be the roots of the equation x 2 + x + 1 = 0 . Then for y ≠ 0 in R , y + 1 α β α y + β 1 β 1 y + α is equal to

Step-by-step solution

Roots of the equation x 2 + x + 1 = 0 are α and β and we know that the sum of roots of a quadratic equation a x 2 + b x + c = 0 is - b a and c a respectively. ⇒ α + β = - 1 and α β = 1 . Now, let ∆ = y + 1 α β α y + β 1 β 1 y + α Applying R 1 → R 1 + R 2 + R 3 , we get ∆ = y + 1 + α + β y + 1 + α + β y + 1 + α + β α y + β 1 β 1 y + α = y + 1 + α + β 1 1 1 α y + β