If a tangent drawn at P α , α 3 to the curve y = x 3 meets it again at Q β , β 3 , then 2 β + α is equal to

Step-by-step solution

Slope of P Q = β 3 - α 3 β - α = d y d x P ⇒ β 2 + α 2 + β α = 3 α 2 ⇒ β 3 + β α - 2 α 2 = 0 ⇒ β + 2 α β - α = 0 ⇒ β = - 2 α   a s   β ≠ α ⇒ 2 β + α = - 4 α + α = - 3 α