\(a)\)\(2x+10\ge0< =>2x\ge-10\\ < =>x\ge-5\)

\(b)\)\(4x^2-36\ge0< =>4x^2\ge36\\ < =>x^2\ge9\\ < =>\left|x\right|\ge3\\ < =>\left[{}\begin{matrix}x\ge3\\x\le-3\end{matrix}\right.\)

\(C=-6x-x^2+12\\ =-\left(x^2+6x-12\right)\\ =-\left[\left(x^2+6x+9\right)-21\right]\\ =-\left(x+3\right)^2+21\le21\)

\(Dấu ''=''\ xảy\ ra \ khi:\)\(\left(x+3\right)^2=0< =>x=-3\)

\(Vậy\ GTLN\ của \ biểu\ thức \ là :21\ khi x=-3\)

\(2x^2+2x+2xy+y^2+6\\ =\left(x^2+2x+1\right)+\left(x^2+2xy+y^2\right)+5\\ =\left(x+1\right)^2+\left(x+y\right)^2+5>=5\\ \)

\(Dấu ''=''\ xảy\ ra\ khi :\)

\(\left\{{}\begin{matrix}x+1=0\\x+y=0\end{matrix}\right.< =>\left(x;y\right)=\left(-1;1\right)\)

\(Vậy \ GTNN\ của \ biểu\ thức \ là :5\ khi \ (x;y)=(-1;1)\)

\(A=x^2-10x-9\\ =\left(x^2-10x+25\right)-34\\ =\left(x-5\right)^2-34>=-34\)

\(Dấu''=''\ xảy\ ra\ khi :\)\(\left(x-5\right)^2=0< =>x=5\)

\(Vậy\ GTNN\ của\ A\ là :-34\ khi\ x=5\)

\(B=x^2+5x-6\\ =x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2-\dfrac{25}{4}-6\\ =\left(x+\dfrac{5}{2}\right)^2-\dfrac{49}{4}>=-\dfrac{49}{4}\)

\(Dấu ''=''\ xảy\ ra\ khi :\)\(\left(x+\dfrac{5}{2}\right)^2=0< =>x=-\dfrac{5}{2}\)

\(Vậy\ GTNN\ của\ B\ là : -49/4\ khi\ x=-5/2\)

\(x^2-5x+6=0\\ a=1;b=-5;c=6\\ =>\Delta=\left(-5\right)^2-4.1.6=25-24=1>0\)

\(=> Phương\ trình\ có\ 2\ nghiệm\ phân\ biệt:\)

\(x_1=\dfrac{-\left(-5\right)+\sqrt{1}}{2.1}=3;x_2=\dfrac{-\left(-5\right)-\sqrt{1}}{2.1}=2\)

\(x^2-5x+6=0\\ < =>\left(x^2-2x\right)-\left(3x-6\right)=0\\ < =>x\left(x-2\right)-3\left(x-2\right)=0\\ < =>\left(x-2\right)\left(x-3\right)=0\\ =>\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.< =>\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.=>S=\left\{2;3\right\}\)

\(x\sqrt{x}-\sqrt{x}+x-1\\ =\sqrt{x}\left(x-1\right)+\left(x-1\right)\\ =\left(x-1\right)\left(\sqrt{x}+1\right)=\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2\)

\(2.5^{x+1}=50\\ =>5^{x+1}=\dfrac{50}{2}=25=5^2\\ =>x+1=2\\ =>x=1\)

\(m=2\ hoặc\ m=-2\ nha\ bạn.\)

\(Để\ đường\ thẳng\ y=(m^2+1)x+m//y=5x+2\ thì:\)

\(\left\{{}\begin{matrix}m^2+1=5\\m\ne2\end{matrix}\right.< =>\left\{{}\begin{matrix}m^2=4\\m\ne2\end{matrix}\right.< =>\left\{{}\begin{matrix}m=\pm2\\m\ne2\end{matrix}\right.< =>m=-2\)