We can use the picking numbers approach here.kaps786 wrote:Is x>0
1. x<x^2
2. x<x^3
Can someone show me how to solve quadratic inequalities particularly how to identify the solutions on the number line.
OA IS E
(1) x < x²
If x = -2, x² = (-2)² = 4, then x < 0.
If x = 2, x² = (2)² = 4, then x > 0.
If x = -1/2, x² = (-1/2)² = 1/4, then x < 0.
No definite answer from the above examples. So statement 1 is NOT sufficient.
(2) x < x^3
If x = 2, x^3 = (2)^3 = 8, then x > 0.
If x = -1/2, x^3 = (-1/2)^3 = -1/8, then x < 0.
No definite answer from the above examples. So statement 2 is NOT sufficient.
Combining (1) and (2), if we take the same examples as taken in statements 1 and 2, x = 2, x = -1/2, then again we do not get a definite answer.
The correct answer is E.
