Equations And Inequalities Question 49
Question: The solution set of the inequality $ {5^{x+2}}>{{( \frac{1}{25} )}^{1/x}} $ is
Options:
A) $ (-2,0) $
B) $ (-2,2) $
C) $ (-5,5) $
D) $ (0,\infty ) $
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] We have $ {5^{x+2}}>{{( \frac{1}{25} )}^{\frac{1}{x}}}\Rightarrow {5^{x+2}}>{5^{-\frac{2}{x}}}\Rightarrow x+2>-\frac{2}{x} $ $ [\because ,base,5>1] $
$ \Rightarrow x+2+\frac{2}{x}>0\Rightarrow \frac{x^{2}+2x+2}{x}>0\Rightarrow \frac{1}{x}>0 $ $ [\because x^{2}+2x+2>0\forall x\in R] $
$ \Rightarrow x>0orx\in (0,\infty ) $
BETA
