id 229272 баллаНеравенстваРешите неравенство −12(x−1)2−2⩾0\cfrac{-12}{(x-1)^2-2} \geqslant 0(x−1)2−2−12⩾0 .Показать решениеРешить похожиеРешениеРешение:−12(x−1)2−2⩾0\cfrac{-12}{(x-1)^2-2} \geqslant 0(x−1)2−2−12⩾0⇒(x−1)2−2<0\Rightarrow (x-1)^2-2<0⇒(x−1)2−2<0, так как −12<0-12<0−12<0 и −12(x−1)2−2⩾0\cfrac{-12}{(x-1)^2-2} \geqslant 0(x−1)2−2−12⩾0 (x−1)2−2<0(x-1)^2-2<0(x−1)2−2<0(x−1)2−(2)2<0(x-1)^2-(\sqrt{2})^2<0(x−1)2−(2)2<0(x−1−2)(x−1+2)<0(x-1-\sqrt{2})(x-1+\sqrt{2})<0(x−1−2)(x−1+2)<0(x−1−2)(x−1+2)=0(x-1-\sqrt{2})(x-1+\sqrt{2})=0(x−1−2)(x−1+2)=0x−1−2=0x-1-\sqrt{2}=0x−1−2=0 или x−1+2=0x-1+\sqrt{2}=0x−1+2=0x=1+2x=1+\sqrt{2 }x=1+2 или x=1−2x=1-\sqrt{2}x=1−2Ответ: x∈(1−2;1+2)x \in (1-\sqrt{2};1+\sqrt{2})x∈(1−2;1+2)