If k^2 = m^2, which of the following must be true?
A. k = m
B. k = -m
C. k = |m|
D. k = - |m|
E. |k| = |m|
A. k = m
B. k = -m
C. k = |m|
D. k = - |m|
E. |k| = |m|
The question asks us what MUST be true. So, if we can find a case where a statement is not true, we can eliminate that answer choice.amina.shaikh309 wrote:If k² = m², which of the following must be true?
A. k = m
B. k = -m
C. k = |m|
D. k = - |m|
E. |k| = |m|
So, for example, one solution to the equation (k² = m²) is k = 1 and m = 1
Now let's check the answer choices.
A. k = m. Test: 1 = 1. Works. Keep A.
B. k = -m. Test: 1 = -1. DOESN'T WORK. ELIMINATE B.
C. k = |m|. Test: 1 = |1|. Works. Keep C.
D. k = - |m|. Test: 1 = -|1|. DOESN'T WORK. ELIMINATE D.
E. |k| = |m|. Test: |1| = |1|. Works. Keep E.
Okay, so the correct answer is A, C or E
Let's try another case. Another solution to the equation (k² = m²) is k = -1 and m = 1
Now let's check the remaining answer choices.
A. k = m. Test: -1 = 1. DOESN'T WORK. ELIMINATE A.
C. k = |m|. Test: -1 = |1|. DOESN'T WORK. ELIMINATE C.
E. |k| = |m|. Test: |-1| = |1|. Works. Keep E.
By the process of elimination, the correct answer is E
Cheers,
Brent
