The fifth term in the expansion of $\left(px - \frac{q}{x}\right)^n$, where $p$ and $q$ a

Question

The fifth term in the expansion of $\left(px - \frac{q}{x}\right)^n$, where $p$ and $q$ are positive numbers, is independent of $x$. Show that $n = 8$.[2] Hence, explain why the fifth term is a positive constant.[1] It is given that $p = 3$ and $q = 1$. Find the term independent of $x$ in $\left(2 + \frac{1}{x^2}\right)\left(px - \frac{q}{x}\right)^n$ for $n = 8$.

Accepted Answer

(a) $n=8$ (shown) (b) $T_5=70p^4q^4>0$, independent of $x$. (c) $-2268$

2024 CGSS P2 Q4

2024 CGSS P2 Q4

Solution:

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