If |x| < x^2, which of the following must be true ?  Choose the most appropriate option:
A) x² >- 1.
B) x² > -2.
C) x² > 0.
D) x² > 1.
E) x² > 2.
|x| &lt; x² implies that x is NONZERO.   Since x is nonzero, |x| &gt; 0 and x² &gt; 0.   Implication:   Both sides of the inequality are positive, allowing us to SQUARE the inequality.   (|x|)² &lt; (x²)²   x² &lt; x⁴.   Since x² &gt; 0, we can safely DIVIDE both sides by x²:   x²/x² &lt; x⁴/x²   1 &lt; x²   x² &gt; 1.   Answer x² &gt; 1.
<result>D</result>
If |x| < x^2, which of the following must be true ?