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## Homework Statement

An exercise in Lang's Basic Mathematics which asked to solve for x in the equation ##(x - 5)^{-2} = 9##

I tried to solve it and got ##x = \frac {16} 3##

which is correct according to the book, but I've found that the book states that x also equals \frac {14}3, and I can't figure out how.

## Homework Equations

## The Attempt at a Solution

##(x-5)^{-2} = 9##

This yields: ##x-5 = 9^{-1/2} =\frac 1 {9^{1/2}} = \frac13##

Which yields: ##x=\frac 13 +5 = \frac {1+15} 3 =\frac {16}3##

But I can't figure out how can x equals ##\frac {14}3## too.