Problem: If x<a<0x<a<0x<a<0 means that xxx and aaa are numbers such that xxx is less than aaa and aaa is less than zero, then
Answer Choices:
A. x2<ax<0x^{2}<a x<0x2<ax<0
B. x2>ax>a2x^{2}>a x>a^{2}x2>ax>a2
C. x2<a2<0x^{2}<a^{2}<0x2<a2<0
D. x2>axx^{2}>a xx2>ax but ax<0a x<0ax<0
E. x2>a2x^{2}>a^{2}x2>a2 but a2<0a^{2}<0a2<0 Solution:
Since x<ax<ax<a and a<0,x2>axa<0, x^{2}>a xa<0,x2>ax and ax>a2.∴x2>ax>a2a x>a^{2} . \quad \therefore x^{2}>a x>a^{2}ax>a2.∴x2>ax>a2.