\(\Leftrightarrow x^2+2x-3,5=0\\ \Leftrightarrow2x^2+4x-7=0\\ \Leftrightarrow2\left(x^2+2x+1\right)-9=0\\ \Leftrightarrow2\left[\left(x+1\right)^2-\dfrac{9}{2}\right]=0\\ \Leftrightarrow\left(x+1-\dfrac{3}{\sqrt{2}}\right)\left(x+1+\dfrac{3}{\sqrt{2}}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{\sqrt{2}}-1=\dfrac{3-\sqrt{2}}{\sqrt{2}}\\x=\dfrac{3}{\sqrt{2}}+1=\dfrac{3+\sqrt{2}}{\sqrt{2}}\end{matrix}\right.\)

\(d,\Delta'=6^2-\left(-2\right)\cdot3=42>0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-6-\sqrt{42}}{3}\\x=\dfrac{-6+\sqrt{42}}{3}\end{matrix}\right.\)

\(e,\Delta'=\left(\sqrt{5}\right)^2-\left(-1\right)\cdot1=6\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-\sqrt{5}-\sqrt{6}}{1}=-\sqrt{5}-\sqrt{6}\\x=\dfrac{-\sqrt{5}+\sqrt{6}}{1}=-\sqrt{5}+\sqrt{6}\end{matrix}\right.\)

\(a,\text{Diện tích tường là }5\cdot4=20\left(m^2\right)=200000\left(cm^2\right)\\ \text{Diện tích cửa sổ và cửa ra vào là }100\cdot100+250\cdot120=40000\left(cm^2\right)\\ \Rightarrow\text{Diện tích tường cần sơn là }200000-40000=160000\left(cm^2\right)=16\left(m^2\right)\\ b,\text{Cần trả }16\cdot20000=320000\left(đồng\right)\)

\(K=\left(\dfrac{10}{3}\cdot\dfrac{19}{10}+\dfrac{19}{2}:\dfrac{13}{3}\right)\cdot\left(\dfrac{62}{75}-\dfrac{12}{25}\right)=\left(\dfrac{19}{3}+\dfrac{57}{26}\right)\cdot\dfrac{2}{3}=\dfrac{665}{78}\cdot\dfrac{2}{3}=\dfrac{665}{117}\)

\(a,A=15x+10+2x-14=17x-4\\ b,\Leftrightarrow x\left(x-9\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=9\end{matrix}\right.\)

\(a,=\left(x+y\right)^2-9=\left(x+y+3\right)\left(x+y-3\right)\\ b,=x\left(2x^2-2x+7x-7\right)=x\left(x-1\right)\left(2x+7\right)\)

\(N=\dfrac{2^6\cdot3^6+2^3\cdot3^3\cdot3^3+3^6}{-73}=\dfrac{3^6\left(2^6+2^3+1\right)}{-73}=\dfrac{3^6\cdot73}{-73}=-3^6=-729\)

\(A=BQ+R\\ \Leftrightarrow A:B=Q\left(\text{dư }R\right)\)

Ta có \(A:B=\left(2x^4+3x^3-5x^2-11x+8\right):\left(x^3-3x+1\right)\)

\(\Leftrightarrow A:B=\left(2x^4-6x^2+2x+3x^3-9x^2+3x+10x^2-16x+8\right):\left(x^3-3x+1\right)\\ \Leftrightarrow A:B=\left[\left(x^3-3x+1\right)\left(2x+3\right)+10x^2-16x+8\right]:\left(x^3-2x+1\right)\\ =2x+3\left(\text{dư }10x^2-16x+8\right)\\ \Leftrightarrow\left\{{}\begin{matrix}Q=2x+3\\R=10x^2-16x+8\end{matrix}\right.\)

\(\dfrac{2b+c-a}{a}=\dfrac{2c-b+a}{b}=\dfrac{2a+b-c}{c}=\dfrac{2\left(a+b+c\right)}{a+b+c}=2\\ \Leftrightarrow\left\{{}\begin{matrix}2b+c-a=2a\\2c-b+a=2b\\2a+b-c=2c\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3a-2b=c\\3b-2c=a\\3c-2a=b\end{matrix}\right.\text{ và }\left\{{}\begin{matrix}3a-c=2b\\3b-a=2c\\3c-b=2a\end{matrix}\right.\\ \Leftrightarrow P=\dfrac{a\cdot b\cdot c}{2a\cdot2b\cdot3c}=\dfrac{1}{8}\)

\(a,\text{Thay }x=-1;y=2\Leftrightarrow-a=2\Leftrightarrow a=-2\)