id 229312 баллаНеравенстваРешите неравенство −14(x−5)2−2⩾0\cfrac{-14}{(x-5)^2-2} \geqslant 0(x−5)2−2−14⩾0 .Показать решениеРешить похожиеРешениеРешение:−14(x−5)2−2⩾0\cfrac{-14}{(x-5)^2-2} \geqslant 0(x−5)2−2−14⩾0⇒(x−5)2−2<0\Rightarrow (x-5)^2-2<0⇒(x−5)2−2<0, так как −14<0-14<0−14<0 и −14(x−5)2−2⩾0\cfrac{-14}{(x-5)^2-2} \geqslant 0(x−5)2−2−14⩾0 (x−5)2−2<0(x-5)^2-2<0(x−5)2−2<0(x−5)2−(2)2<0(x-5)^2-(\sqrt{2})^2<0(x−5)2−(2)2<0(x−5−2)(x−5+2)<0(x-5-\sqrt{2})(x-5+\sqrt{2})<0(x−5−2)(x−5+2)<0(x−5−2)(x−5+2)=0(x-5-\sqrt{2})(x-5+\sqrt{2})=0(x−5−2)(x−5+2)=0x−5−2=0x-5-\sqrt{2}=0x−5−2=0 или x−5+2=0x-5+\sqrt{2}=0x−5+2=0x=5+2x=5+\sqrt{2 }x=5+2 или x=5−2x=5-\sqrt{2}x=5−2Ответ: x∈(5−2;5+2)x \in (5-\sqrt{2};5+\sqrt{2})x∈(5−2;5+2)