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What are the values of y which satisfy the equation \(9^{y} ...

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 is D

\(9^{y} - 4 \times 3^{y} + 3 = 0\)

\(\equiv (3^{2})^{y} - 4 \times 3^{y} + 3 = 0\)

\((3^{y})^{2} - 4 \times 3^{y} + 3 = 0\)

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, \(3^{y} = r\)

\(3^{y} = 3 = 3^{1} \text{ or } 3^{y} = 1 = 3^{0}\)

\(\implies \text{y = 1 or 0}\)