inequalities

[Guest]

prove the following inequality:

[tex]3^x+4^x=2[/tex]

[nathi123]

For x = 0 [tex]\Rightarrow 3 ^{0 }+4 ^{0 }= 2[/tex] If [tex]f(x) = 3 ^{x } +4 ^{x} \Rightarrow f '(x) = 3 ^{x }ln3 +4 ^{x} ln4>0[/tex] for each x [tex]\Rightarrow f(x) - growing[/tex] function for each x
[tex]\Rightarrow x = 0[/tex] is the only solution of the equation