What are the values of y which satisfy the equation (9^{y} – 4 times 3^{y} + 3 = 0) ?
-
A.
-1 and 0 -
B.
-1 and 1 -
C.
1 and 3 -
D.
0 and 1
Correct Answer: Option D
Explanation
(9^{y} – 4 times 3^{y} + 3 = 0)
(equiv (3^{2})^{y} – 4 times 3^{y} + 3 = 0)
((3^{y})^{2} – 4 times 3^{y} + 3 = 0)
Let (3^{y}) be r. Then,
(r^{2} – 4r + 3 = 0)
Solving the equation,
(r^{2} – 3r – r + 3 = 0)
(r(r – 3) – 1(r – 3) = 0)
((r – 3)(r – 1) = 0)
(therefore text{r = 3 or 1})
Recall, (3^{y} = r)
(3^{y} = 3 = 3^{1} text{ or } 3^{y} = 1 = 3^{0})
(implies text{y = 1 or 0})