1) If x<0 , what is square root of -x|x|
And answer choices are:
-x,x,1,0 and square root of x
Given x<0:
-x is a positive number.
|x| is a positive number
Therefore, we can simplify the expression "-x|x|" as x^2. The square root of x^2 = the positive and negative values of the given variable (x). We were told initially that x<0, so the only valid root is the negative one, or -x.
This is a confusing question because, in the beginning, we interpret "-x" to be a positive number, since we know x is negative. And then, at the end, we use that same "-x" to mean the negative value of the number. Looks the same - but it isn't. Try it with real numbers
x < 0. SQRT - (-2)*|-2| = SQRT 2*2 = SQRT 4 = +/- 2 If x is negative, then only -2 is the valid root. See, with these number, how the first "-x" [-(-2)] isn't the same thing as the second "-x" [-2]?