Question

sa se rezolve in multimea nr intregi inecuatia x2-5x+5≤1

Answer 1

$x^2-5x+5 \leq 1 \\ \\ x^2-5x+4 \leq 0 \\ \\ x^{2} -x-4x+4 \leq0 \\ \\ x(x-1)-4(x-1) \leq 0 \\ \\ (x-1)(x-4 ) \leq 0 \Rightarrow$


$\Rightarrow Cazul~1:~(x-1)=0 \Rightarrow x=1. \\ \\ \Rightarrow Cazul~2:~(x-4)=0 \Rightarrow x=4. \\ \\ \Rightarrow Cazul~3:~x-1\ \textless \ 0~si~x-4\ \textgreater \ 0,~imposibil. \\ \\ \Rightarrow Cazul~4:~x-1\ \textgreater \ 0~si~x-4\ \textless \ 0 \Rightarrow x \in(1;4). \\ \\ Solutie:~x \in \{{1,2,3,4\}.$