Решите неравенство: (x^2-6x+8)^2<-x^2+6x-8.

Ответ:

\[\left( x^{2} - 6x + 8 \right)^{2} < - x^{2} + 6x - 8\]

\[\left( x^{2} - 6x + 8 \right)^{2} > x^{2} - 6x + 8\]

\[\left| x^{2} - 6x + 8 \right| > x^{2} - 6x + 8\]

\[1)\ при\ x > 0:\]

\[x^{2} - 6x + 8 > x^{2} - 6x + 8\]

\[0x > 0\]

\[x - любое\ число.\]

\[2)\ при\ x < 0:\]

\[- x^{2} + 6x - 8 > x^{2} - 6x + 8\]

\[- 2x^{2} + 12x - 16 > 0\]

\[x^{2} - 6x + 8 < 0\]

\[D_{1} = 9 - 8 = 1\]

\[x_{1} = 3 + 1 = 4;\]

\[x_{2} = 3 - 1 = 2.\]

\[(x - 2)(x - 4) < 0.\]

\[2 < x < 4.\]

\[Ответ:2 < x < 4.\]