Bunuel wrote:
If \(2*y^{-2} + 3*y^{-1} - 14 = 0\), which of the following could be the value of y?
A. 2
B. 1/2
C. 2/7
D. -1/2
E. -7
Simplifying we have:
2/y^2 + 3/y - 14 = 0
Multiplying by y^2 we have:
2 + 3y - 14y^2 = 0
14y^2 - 3y - 2 = 0
(7y + 2)(2y - 1) = 0
7y + 2 = 0 → y = -2/7
2y - 1 = 0 → y = 1/2
Since only 1/2 is given as one of the choices. Choice B is the correct answer.
Alternate solution:
If we let x = y^-1, then the equation can be rewritten as 2x^2 + 3x - 14 = 0. Let’s solve it:
(2x + 7)(x - 2) = 0
2x + 7 = 0 → x = -7/2
x - 2 = 0 → x = 2
Since x = y^-1 = 1/y, y = 1/x. Therefore, y is either 1/(-7/2) = -2/7 or 1/2. Since only 1/2 is given as one of the choices. Choice B is the correct answer.
Answer: B