Gọi 3 số TN liên tiếp là n-1; n; n+1ta có

\(n.\left(n-1\right)+n.\left(n+1\right)+\left(n-1\right).\left(n+1\right)=146\)

\(\Leftrightarrow n^2-n+n^2+n+n^2-1=146\)

\(\Leftrightarrow3.n^2-1=146\Leftrightarrow3.n^2=147\Leftrightarrow n^2=49\Rightarrow n=7\)

3 số TN liên tiếp là: 5; 7; 9

      \(2x^2-4x+4xy+4y^2+4=0\)

\(\Rightarrow\left(x^2-4x+4\right)+\left(x^2+4xy+4y^2\right)=0\)

\(\Rightarrow\left(x^2-2.x.2+2^2\right)+\left(x^2+2.x.2y+\left(2y\right)^2\right)=0\)

\(\Rightarrow\left(x-2\right)^2+\left(x+2y\right)^2=0\)

\(\Rightarrow\hept{\begin{cases}x-2=0\\x+2y=0\end{cases}\Rightarrow}\hept{\begin{cases}x=2\\y=-1\end{cases}}\)

Chúc bạn học tốt.

\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)

\(=\left[xy\left(x+y\right)+xyz\right]+\left[yz\left(y+z\right)+xyz\right]+xz\left(x+z\right)\)

\(=xy\left(x+y+z\right)+yz\left(x+y+z\right)+xz\left(x+z\right)\)

\(=y\left(x+y+z\right)\left(x+z\right)+xz\left(x+z\right)\)

\(=\left(x+z\right)\left(x^2+y^2+yz+xz\right)\)

\(=\left(x+z\right)\left(x+y\right)\left(y+z\right)\)

\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz.\)

\(=x^2y+xy^2+x^2z+xz^2+2xyz+yz\left(y+z\right)\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2+2yz\right)+yz\left(y+z\right)\)

\(=x^2\left(y+z\right)+x\left(y+z\right)^2+yz\left(y+z\right)\)

\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)

\(=\left(y+z\right)\left[x\left(x+z\right)+y\left(x+z\right)\right]=\left(y+z\right)\left(x+y\right)\left(x+z\right)\)