Question

The set of possible values of $x$ such that $\left(5^x+(2\sqrt{3}{)}^{2x}-169\right)$ is always positive, is

• A. $[3,+\infty )$
• B. $[2,+\infty )$
• C. $(2,+\infty )$
• D. none of these

Answer 1

Answer: (C)

$(2,+\infty )$

$5^x+(2\sqrt{3}{)}^{2x}-169>0$

$\Rightarrow 5^x+(12{)}^x>169...(1)$

using Pythagorean (1) is only possible for

$x>2$

Hence $xϵ(2,\alpha )$

Hence Option C is correct