Решите систему неравенств: а)[latex] \left \{ {{2x+4\ \textgreater \ 0} \atop {x^2+2x-3 \geq 0}} \right. [/latex] б)[latex] \left \{ {{2x^2 \leq 32} \atop {x^2-4x+3 \geq 0}} \right. [/latex]

Question

Решите систему неравенств: а)[latex] \left \{ {{2x+4\ \textgreater \ 0} \atop {x^2+2x-3 \geq 0}} \right. [/latex] б)[latex] \left \{ {{2x^2 \leq 32} \atop {x^2-4x+3 \geq 0}} \right. [/latex]

Гость

Ответ(ы) на вопрос:

Accepted Answer

{2x+4>0⇒2x>-4⇒x>-2 {x²+2x-3≥0⇒x≤-3 U x≥1 x1+x2=-2 U x1*x2=-3⇒x1=-3 U x2=1 x∈[1;∞) {2x²≤32⇒2(x-4)(x+4)≤0⇒-4≤x≤4 {x²-4x+3≥0⇒x≤1 U x≥3 x1+x2=4 U x1*x2=3⇒x1=1 U x2=3 x∈[-4;1] U [3;4]