Ta có \(87x+191y=987x-900x+1991y-1800y\)

\(\Leftrightarrow87x+191y=\left(987x+1991y\right)-9\left(100x+200y\right)\)

Ta có \(9\left(100x+200y\right)⋮9;\left(987x+1991y\right):9R2\)

\(\Rightarrow\left(87x+191y\right):9R2\)

\(S=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+\left(3^7+3^8+3^9\right)\\ S=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+3^7\left(1+3+3^2\right)\\ S=\left(1+3+3^2\right)\left(3+3^4+3^7\right)=13\left(3+3^4+3^7\right)⋮13\)

\(=\dfrac{2\left(\sqrt{3}+\sqrt{2}\right)}{3-2}+\dfrac{3-2\sqrt{2}}{9-8}=2\sqrt{3}+2\sqrt{2}+3-2\sqrt{2}=3+2\sqrt{3}\)

\(ĐK:x\ne2;x\ne-3\\ PT\Leftrightarrow\left(x-2\right)\left(x+3\right)+2\left(x+3\right)=10\left(x-2\right)+50\\ \Leftrightarrow x^2+x-6+2x+6=10x-20+50\\ \Leftrightarrow x^2-13x-30=0\\ \Leftrightarrow x^2-15x+2x-30=0\\ \Leftrightarrow\left(x-15\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=15\\x=-2\end{matrix}\right.\left(tm\right)\)

Vì 2 đt cắt trên trục Ox nên \(y=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(m-3\right)x+m^2+7=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2\left(m-3\right)+m^2+7=0\\x=2\end{matrix}\right.\\ \Leftrightarrow2m-6+m^2+7=0\\ \Leftrightarrow\left(m+1\right)^2=0\Leftrightarrow m=-1\)

\(a,=2x\left(x-7\right)\\ b,=\left(x-1\right)^2:\left(x-1\right)=x-1\\ c,\Rightarrow5x=8-12=-4\Rightarrow x=-\dfrac{4}{5}\)

\(d,=\dfrac{4\left(1-\sqrt{5}\right)}{\sqrt{2}\left(1-\sqrt{5}\right)}=2\sqrt{2}\\ e,=\dfrac{\sqrt{2}\left(\sqrt{3}-1\right)}{3\left(\sqrt{3}-1\right)}=\dfrac{\sqrt{2}}{3}\\ f,=\dfrac{3\cdot2\sqrt{5}}{2^2\cdot5}=\dfrac{6\sqrt{5}}{20}=\dfrac{3\sqrt{5}}{10}\)

\(=\sqrt{\dfrac{\left(3-\sqrt{5}\right)^2}{9-5}}+\sqrt{\dfrac{\left(3+\sqrt{5}\right)^2}{9-5}}=\dfrac{3-\sqrt{5}}{2}+\dfrac{3+\sqrt{5}}{2}=\dfrac{6}{2}=3\)

\(=\dfrac{\sqrt{\left(m^2-4\right)}}{m-1}=\dfrac{\left|m^2-4\right|}{m-1}=\dfrac{\left|4-2\sqrt{3}-4\right|}{1-\sqrt{3}-1}=\dfrac{2\sqrt{3}}{-\sqrt{3}}=-2\)