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radical sign x-1 = x-3
The radical sign is only by x-1
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√x-1 = x-3
Square both sides
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(√x - 1)² = (x - 3)²
When you square a square root, you
take away the radical
x - 1 = (x - 3)²
Now you square the right side by writing
(x - 3)² as (x - 3)(x - 3)
x - 1 = (x - 3)(x - 3)
You finish it! It will become a quadratic
equation. You will get solutions 2 and 5
However you must ALWAYS check radical equations!
You will find that the 2 does not check in the
original equation, but the 5 does check.
So you discard the 2 solution as an extraneous
solution, and the only correct solution is 5.
Edwin
