Given that the constant term in the binomial expansion of $\left(x-\frac{k}{x^3}\right)^8$ is \(7\

Question

Given that the constant term in the binomial expansion of $\left(x-\frac{k}{x^3}\right)^8$ is $7$, find the value of the positive constant $k$.[4] Using the value of $k$ found in part (a), show that there is no constant term in the expansion of $(1+x^4)\left(x-\frac{k}{x^3}\right)^8$.[4]

Accepted Answer

(a) $k=\frac12$ (b) $7+x^4(-7x^{-4})=7-7=0$, so there is no constant term.

2025 DSS PRELIMS P2 Q5

2025 DSS PRELIMS P2 Q5

Solution:

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