(x-2)^(x²-6x+8)>1
(x-2)^(x²-6x+8)>(x-2)⁰
1. пусть х-2>1. x>3,
тогда x²-6x+8>0. x²-6x+8=0. x₁=2,x₂=4
+ - +
-----------(2)-----------(4)---------------->x
x∈(-∞;2)U(4;∞)
/ / / / / / / / / / / / / / / /
--------------(2)----------(3)----------(4)---------->x
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
x∈(4;∞)
2. пусть 0<х-2<1, 2<x<3<br>тогда, x²-6x+8<0<br>x∈(2;4)
/ / / / / / / / / / / / / /
----------(2)-------(3)----------(4)---------->x
\ \ \ \ \ \ \
x∈(2;3)
ответ: x∈(2;3)U(4;∞)