If ^x C2 = 4[^x Cx-1], find the values of x.

Here are the solutions to the mathematics questions.

9. (a) If $^x C_2 = 4[^x C_{x-1}]$, find the values of $x$.

Step 1: Use the combination formula $^n C_r = \frac{n!}{r!(n-r)!}$ and the property $^n C_r = ^n C_{n-r}$.
We are given $^x C_2 = 4[^x C_{x-1}]$.
Using the property, $^x C_{x-1} = ^x C_{x-(x-1)} = ^x C_1$.
So the equation becomes:

$$^x C_2 = 4(^x C_1)$$