Problem:
Which expression is equal to
∣∣∣∣a−2−(a−1)2∣∣∣∣
for a<0?
Answer Choices:
A. 3−2a
B. 1−a
C. 1
D. a+1
E. 3
Solution:
Because a is negative, a−1<0, so (a−1)2=∣a−1∣=1−a. Therefore distributing gives a−2−(1−a)=2a−3. Because a is negative, 2a−3<0, so ∣2a−3∣=(A)3−2a.
The problems on this page are the property of the MAA's American Mathematics Competitions