Problem: The relation x2(x2−1)≧0 is true for:
Where x≧ a means that x can take on all values greater than a and the value equal to a, while x≦a has a corresponding meaning with "less than."
Answer Choices:
A. x≧1 only
B. −1≦x≦1
C. x=0,x=1,x=−1
D. x=0,x≦−1,x≧1
E. x≧0 only
Solution:
First note that the equality x2(x2−1)=0 is satisfied by 0,0,+1,−1. Since x2 is non-negative, then x2(x2−1)>0 implies x2−1>0. ∴x2>1; ∴∣x∣>1, that is, x>1 or x<−1. Combining these, we have x=0,x≤−1,x≥1.