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Question
Answer the following:
Suppose (1 + kx)n = 1 − 12x + 60x2 − .... find k and n.
Solution
(1 + kx)n = 1 − 12x + 60x2 − ...
∴ `1 + ("nk")x + ("n"("n" - 1))/2 "k"^2x^2 + ...` = 1 − 12x + 60x2 + ...
Equating the coefficients on both sides, we get
∴ nk = − 12 ...(i)
and `("n"("n" - 1))/2 "k"^2` = 60 ...(ii)
∴ n2k2 – nk2 = 120
∴ 144 – (nk)k = 120 …[From (i)]
∴ 144 – 120 = –12k …[From (i)]
∴ k = `-24/12` = − 2
Substituting the value of k in equation (i), we get
n = `(-12)/"k"`
= `(-12)/(-2)`
= 6
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