c: Gọi bốn số nguyên liên tiếp là x;x+1;x+2;x+3
Ta có: \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)
\(=\left(x^2+3x\right)\left(x^2+3x+2\right)+1\)
\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)+1\)
\(=\left(x^2+3x+1\right)^2\)
\(d,M=\left(x^2-4xy+4y^2\right)-2\left(x-2y\right)+1+9\\ M=\left(x-2y\right)^2-2\left(x-2y\right)+1+9\\ M=\left(x-2y+1\right)^2+9\ge9\\ M_{min}=9\Leftrightarrow x=2y-1\)
\(a,a^3+b^3+c^3=3abc\\ \Leftrightarrow a^3+b^3+c^3-3abc=0\\ \Leftrightarrow\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)=0\left(luôn.đúng.do.a+b+c=0\right)\)
\(b,x^2-2xy+6y^2-12x+2y+41=0\\ \Leftrightarrow\left(x-y\right)^2-12\left(x-y\right)+36+5y^2-10y+5=0\\ \Leftrightarrow\left(x-y-6\right)^2+5\left(y-1\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x=y+6\\y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=7\\y=1\end{matrix}\right.\)
\(A=\dfrac{2020-2019\left(9-7-1\right)^{2019}-\left(7-6\right)^{2018}}{1^{2020}}\\ A=2020-2019\cdot1-1^{2018}=2020-2019-1=0\)
bài 2 câu 1,2,3,5,9 
