If \(^{3x}C_{2} = 15\), find the value of x?
FURTHER MATHEMATICS
WAEC 2011
If \(^{3x}C_{2} = 15\), find the value of x?
- A. 2
- B. 4
- C. 5
- D. 6
Correct Answer: A. 2
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.
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