DevS93 wrote:
6. (Book Question: 90)
If x = –|w|, which of the following must be true?
A. x = –w
B. x = w
C. x2 = w
D. x^2 = w^2
E. x3 = w3
I picked A.
because if x= –|w|,
then x +|w|=0
That means that since |w| is always positive, X must always be negative and equal to -w for the above condition to be true i.e. ( -w+|w| =0)
Given x = –|w|.
Arrange the equation and plug the values.
Absolute value properties:
When x≤0 then |x|=−x, or more generally when some expression≤0 then |some expression|=−(some expression). For example: |−5|=5=−(−5)
When x≥0 then |x|=x, or more generally when some expression≥0 then |some expression|=some expression. For example: |5|=5|5|=5Then x + |w| = 0 is the question. Here we are not sure whether w has to be postive or negative. Follow the above property.
x or w has to be negative ( for ex x = 2 and w = -2 then we get 0 )
1. x= - w.
=> x + w = 0. if w ≤ 0 ; then w = -ve ; then we get 0 total.
if w > 0 ; then w = +ve ; then we get some total.
Not true. Two different answers.
2. x = w.
Same as the above explanation, depending upon w as +ve or -ve value we get 0 or some total.
3. \(x^2\) = w. Same as above explanation.
4. \(x^2\) = \(w^2\) .
Then \(x^2\) - \(w^2\) if the result has to be 0 then consider w = +ve or -ve , in both the cases we get 0 as the result. ( ex: x = 2 or w = +2/-2) .
5. \(x^3\) - \(w^3\) ; when w = +ve we get 0 as the result or when w = -ve we some total. For ex: ( \(2^3\) - \((-2)^3\) = 16 ).
For the 5th option I think it has to be x power cube and w power cube.