7.
\((1)\)若命题“\(∃x∈R,{x}^{2}+\left(a-1\right)x+1 < 0 \)”是假命题,则实数\(a\)的取值范围是_______.
\((2)\)若\(x\),\(y\)满足约束条件\({ }\!\!\{\!\!{ }\begin{matrix} 2x-y-1\leqslant 0, \\ 2x+y-7\leqslant 0, \\ x\geqslant 1, \\\end{matrix}{ }\)则\(\dfrac{y}{x+1}\)的取值范围为__________.
\((3)\)已知\(p\):\(4\leqslant 2x\leqslant 12\),\(q\):\(x^{2}-2x+1-m^{2}\leqslant 0(m > 0)\),若\(¬ p\)是\(a,b,cq\)的必要而不充分条件,则实数\(m\)的取值范围是
\((4)\)已知\(a,b,c\)为正实数,给出以下命题:\(①\)若\(a-2b+3c=0\),则\(\dfrac{{{b}^{2}}}{ac}\)的最小值是\(3\);\(②\)若\(a+2b+2ab=8\),则\(a+2b\)的最小值是\(4\);\(③\)若\(a\left( a+b+c \right)+bc=4\),则\(2a+b+c\)的最小值是\(2\sqrt{2}\);\(.\)其中正确结论的序号是 .