JAMB - Mathematics (1993 - No. 4)
If 9\(^{(x - \frac{1}{2})} = 3^{x^2}\) Find the value of x
\(\frac{1}{2}\)
1
2
3
Explanation
9(x - \(\frac{1}{2}\)) 3x2 = 3\(^{2(x - \frac{1}{2})}\) = 3\(^x{^2}\)
∴ 2(x - \(\frac{1}{2}\)) = x2
2x - 1 = x\(^2\)
hence x\(^2\) - 2x + 1 = 0
(x - 1)(x - 1) = 0
x = 1
∴ 2(x - \(\frac{1}{2}\)) = x2
2x - 1 = x\(^2\)
hence x\(^2\) - 2x + 1 = 0
(x - 1)(x - 1) = 0
x = 1
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