Question

rezolvati ecuatia: (x-3)[5(x+5)-6(x+3)] ≤ 0

Answer 1

$(x-3)[5(x+5)-6(x+3)] \leq 0 \\\\ (x-3)(5x+25-6x-18) \leq 0 \\\\ (x-3)(-x+7) \leq 0 \\\\ -x^2+7x+3x-7 \leq 0 \\\\ -x^2+10x-7 \leq 0 \ \ |(-1) \\\\ x^2-10x+7 \geq 0 \\\\ \hbox{Cautam valori pentru x pentru a fi adevarata relatia:} \\\\ Pt \ x=9 \to 81-90+7 \geq 0 \ \ \ \textless \ =\ \textgreater \ 88-90 \geq 0 \ \ 'F' \\\\ x=10 \to 100-100+7 \geq 0 \ \ \ \textless \ =\ \textgreater \ \ 7 \geq 0 \ \ 'A' \\\\ x=11 \to 121-110+7 \geq 0 \ \ \ \textless \ =\ \textgreater \ 128-110 \geq 0 \ \ 'A' \\.\\.\\. \\\\+ \infty \\\\\ \hbox{Multimea solutiilor ecuatiei este:} \to S \in [7; + \infty)$