If 3^2x+9=10(3^x), then the value of x^2+1 is:

1972 AMC 12 Problem 6

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3^{2x}+9=10(3^x),

then the value of

x^2+1

is:

1

only

5

only

1

5

2

10

Set

u=3^x

Factor

u^2-10u+9

and convert each positive root back to

x

Let

u=3^x.

Then

\begin{aligned} u^2-10u+9&=(u-1)(u-9)\\ &=0. \end{aligned}

Thus

x=0

x=2,

x^2+1

is respectively

1

5.

Therefore, the correct answer is C.