Answer:
Option C
Step-by-step explanation:
Given 0.5≤ x ≤ 0.7
According to the range of x, we will check which option is true
Let x = 0.6
A. [tex]\frac{x}{3} > \sqrt{x}[/tex]
If x = 0.6
∴0.6/3 > √0.6 ⇒ 0.2 > 0.77 ⇒ Wrong inequality
B. x³ > 1/x
If x = 0.6
∴ 0.6³ > 1/0.6 ⇒ 0.216 > 1.667 ⇒ Wrong inequality
C. √x > x³
If x = 0.6
∴ √0.6 > 0.6³ ⇒ 0.77 > 0.216 ⇒ True inequality
D. (x/3) > (1/x)
If x = 0.6
∴ 0.6/3 > 1/0.6 ⇒ 0.2 > 1.667 ⇒ Wrong inequality
So, The true inequality is option C
