Problems need HardWork #10

$\large{4^x+4^{\frac{1}{x}}=18 \Rightarrow 4^x+4^{\frac{1}{x}}-18=0 }$

$\large{4^x+4^{\frac{1}{x}}-16-2 =0}$

$\large{\Rightarrow 4^x-16=0 \Rightarrow x=\boxed{2}}$

or

$\large{4^{\frac{1}{x}}-2=0 \Rightarrow 2^{2\times\frac{1}{x}}=2^1 \Rightarrow x=\boxed{\frac{1}{2}}}$

Take $\large{2+ \frac{1}{2}=\boxed{\color{#D61F06}{\frac{5}{2}}}}$

Clearly, x = 2 or 1/2.

So, 2 + 0.5 = 2.5