If (^{3x}C_{2} = 15), find the value of x?
-
A.
2 -
B.
4 -
C.
5 -
D.
6
Correct Answer: Option A
Explanation
(^{3x}C_{2} = frac{3x(3x – 1)(3x – 2)!}{(3x – 2)! 2!} = 15)
(3x(3x – 1) = 30 implies 9x^{2} – 3x – 30 = 0)
(9x^{2} – 18x + 15x – 30 = 9x(x – 2) + 15(x – 2) = 0)
((9x + 15)(x – 2) = 0)
x = 2.