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# a very simply maths question - I'm doing maths whilst tired. watch

1. Yeah I know maths and tiredness don't work well togeather.

Now;

-2 < 1 + (1+x)^2 <2

-3 < (1+x)^2 <1 , understood ofcourse

but now the next step is apparently;

-1 < 1+x <1

but you can't take the roots because the lower limit on the interval is negative?

2. bump
3. ok I think I've figured it out:

since (x+1)^2>0 (a condition is that x>0) then |(x+1)^2|<1 if (x+1)^2 <1
.
So -1 < (x+1)^2 <1

therefore since |(x+1)^2| = |(x+1)|^2 < 1 implies |(x+1)| <1 which leads to -1<x+1<1 and so -2<x<0

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Updated: March 20, 2011
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