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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 9y4×3y+3=0 ?

A.

-1 and 0

B.

-1 and 1

C.

1 and 3

D.

0 and 1

Correct answer is D

9y4×3y+3=0

(32)y4×3y+3=0

(3y)24×3y+3=0

Let 3y be r. Then,

r24r+3=0

Solving the equation, 

r23rr+3=0

r(r3)1(r3)=0

(r3)(r1)=0

Recall, 3^{y} = r

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

\implies \text{y = 1 or 0}