solve $3^x +4^x = 5^x$ in $\Bbb R$ solve the following equation :
$$3^x +4^x = 5^x \text{ in } \Bbb R$$
the trivial answer is $x=2$ .

$$\left( \frac{3}{5} \right)^x+\left( \frac{4}{5} \right)^x=1$$
Then $x=2$
$f(x)=\left( \frac{3}{5} \right)^x+\left( \frac{4}{5} \right)^x$decreasing function
