id 229172 баллаНеравенстваРешите неравенство (x−1)2<2(x−1)(x-1)^2<\sqrt{2}(x-1)(x−1)2<2(x−1) .Показать решениеРешить похожиеРешениеРешение:(x−1)2−2(x−1)<0(x-1)^2-\sqrt{2}(x-1)<0(x−1)2−2(x−1)<0(x−1)(x−1−2)<0(x-1)(x-1-\sqrt{2})<0(x−1)(x−1−2)<0(x−1)(x−1−2)=0(x-1)(x-1-\sqrt{2})=0(x−1)(x−1−2)=0x−1=0x-1=0x−1=0 или x−1−2=0x-1- \sqrt{2}=0x−1−2=0x=1x=1x=1 или x=1+2x=1+ \sqrt{2}x=1+2Ответ: x∈(1;1+2)x \in (1;1+\sqrt{2})x∈(1;1+2)