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Unread 09-08-2005, 10:57
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Re: impossible statements

Quote:
Originally Posted by mechanicalbrain
[ (n+1) - 1/2(2n+1) ]^2 = [ n - 1/2(2n+1) ]^2

Taking the square roots of both sides:
I hate it when square roots go bad.

Seriously, there are times when you have to remember that there is usually more than one root for a given expression. For example, the square roots of 9 are 3 and -3.

If you evaluate the expressions inside the brackets, you find that they can be reduced to 1/2 on the left side and -1/2 on the right. Naively taking the square root of their squares loses the minus sign, and breaks the equality. A proper result at this step requires an arbitrary choice of the negative root for one of the sides of the equation.
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