By the binomial theorem,
^n=\sum_{k-0}^{n}\binom{n}{k}3^{n-k}(-x)^k=\sum_{k-0}^{n}\binom{n}{k}3^{n-k}(-1)^kx^k)
.
The (-1)
k tells us that the signs of the terms alternate, so we only need to focus on the magnitude. The above formula tells us that the coefficient of
xk has magnitude
!}\cdot 3^{n-k})
.
Therefore, the absolute value of the coefficient of
x4 and
x5 are
!}\cdot 3^{n-4})
and
!}\cdot 3^{n-5})
.
Since we want these to be equal, we have