Question

Решите неравенство
|x²-4x+3|≤x-1

Answer 1

$|x^{2}-4x+3|leq x-1$

$-(x-1)leq x^{2}-4x+3leq x-1$

$left { {{x^2-4x+3leq x-1} atop {x^2-4x+3geq -x+1}} right.$

$left { {{x^2-4x+3-x+1leq 0} atop {x^2-4x+3+x-1geq 0}} right.$

$left { {{x^2-5x+4leq 0} atop {x^2-3x+2geq 0}} right.$

$left { {{1leq xleq 4} atop {xleq 1;xgeq 2}} right.$

Общее решение:

$x$ ∈ {$1$}∪[2; 4]