If α and β , be the coefficients of x 4 and x 2 , respectively in the expansion of x + x 2 - 1 6 + x - x 2 - 1 6 , then

Question

If α and β , be the coefficients of x 4 and x 2 , respectively in the expansion of x + x 2 - 1 6 + x - x 2 - 1 6 , then, α + β = 60, α + β = - 30, α - β = 60, α - β = - 132

MARKS App · Accepted Answer

x + x 2 - 1 6 + x - x 2 - 1 6 = 2 C 0 x 6 + C 2 x 4 x 2 - 1 + C 4 x 2 x 2 - 1 2 + C 6 x 2 - 1 3 = 2 x 6 + 15 x 6 - x 4 + 15 x 2 x 4 - 2 x 2 + 1 + - 1 + 3 x 2 - 3 x 4 + x 6 = 2 32 x 6 - 48 x 4 + 18 x 2 - 1 Now given that α & β are the coefficients of x 4 & x 2 respectively, hence α = - 96 and β = 36 ∴ α - β = - 132

Search any question & find its solution

Looking for more such questions to practice?