dave13 wrote:
but two negative signs next to each other give positive value √[1−[color=#0000ff]√(-ve)
so it should be positive i.e. 1 - (- any value) = positive
whats flaw in my reasoning ?
IanStewart maybe you can help
You seem to be suggesting that \(-\sqrt{-x} \) is equal to \(\sqrt{-(-x)}\), but that is absolutely never true unless x is zero. You can never move negative signs in and out of square roots, because then at some point you have a negative number under your square root, and that is mathematically illegal.
And I'd add: the post you quote is not generally correct when it says "Such questions require us to check the smallest or highest values among option". It happens to be true in this particular question that one of the extreme choices is the right answer, but it is very easy to design a similar question where the right answer is in the middle of the choices, e.g.:
For which of the following values of x is the expression \(\sqrt{x^2 - 5}\) undefined?
A) -10
B) -5
C) 0
D) 5
E) 10
The right answer here is C.
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