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\(xy^2-9x=x.\left(y^2-3^2\right)=x.\left(y-3\right)\left(y+3\right)\)
\(x^2+14x+49-y^2=\left(x^2+2.7x+7^2\right)-y^2=\left(x+7\right)^2-y^2=\left(x+7-y\right).\left(x+7+y\right)\)
\(xy-y^2-x+y=y.\left(x-y\right)-\left(x-y\right)=\left(x-y\right).\left(y-1\right)\)
\(5x.\left(x-7\right)-x+7=5x.\left(x-7\right)-\left(x-7\right)=\left(x-7\right).\left(5x-1\right)\)
\(x^2-y^2+5x-5y=\left(x-y\right)\left(x+y\right)+5\left(x-y\right)=\left(x-y\right).\left(x+y+5\right)\)
\(5x^3-40=5.\left(x^3-2^3\right)=5.\left(x-2\right).\left(x^2+2x+4\right)\)
\(x^2-y^2+12y-36=\left(y^2-2.6y+6^2-x^2\right)=-\left[\left(y-6\right)^2-x^2\right]\)\(=-\left[y-6-x\right].\left[y-6+x\right]\)
\(x^2z+4xyz+4y^2z=z.\left[x^2+2.2xy+\left(2y\right)^2\right]=z.\left(x+2y\right)^2\)
a. \(x^2+4y^2+z^2=2x+12y-4z-14\)
\(\Leftrightarrow x^2+4y^2+z^2-2x-12y+4z+14=0\)
\(\Leftrightarrow\left(x^2-2x+1\right)+\left(4y^2-12y+9\right)+\left(z^2+4z+4\right)=0\)
\(\Leftrightarrow\left(x-1\right)^2+\left(2y-3\right)^2+\left(z+2\right)^2=0\)
Ta có: \(\left\{{}\begin{matrix}\left(x-1\right)^2\ge0\\\left(2y-3\right)^2\ge0\\\left(z+2\right)\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-1=0\\2y-3=0\\z+2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=\dfrac{3}{2}\\z=-2\end{matrix}\right.\)
b. \(x^2+3y^2+2z^2-2x+12y+4z+15=0\)
\(\Leftrightarrow\left(x^2-2x+1\right)+3\left(y^2+4y+4\right)+2\left(z^2+2z+1\right)=0\)
\(\Leftrightarrow\left(x-1\right)^2+3\left(y+2\right)^2+2\left(z+1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-1=0\\y+2=0\\z+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\\z=-1\end{matrix}\right.\)
Chia nhỏ ra bạn ơi!
\(a) x² +3y²+2z²-2x+12y+4z+15=0 \)
\(⇔x²-2x+1+3y²+12y+12+2z²+4z+2=0 \)
\(⇔(x²-2x+1) + 3(y²+4y+4) +2(z²+2z+1)=0 \)
\(⇔(x-1)² +3(y+2)²+2(z+1)²=0 \)
\(⇔ x-1=0 \) và \(y+2=0\) và \(z+1=0\)
Vậy: \(x=1;y=-2;z=-1\)
a) \(=2x\left(x-25\right)\)
b) \(=x\left(x-4\right)-\left(x-4\right)=\left(x-4\right)\left(x-1\right)\)
c) \(=x^2-\left(y^2-12y+36\right)=x^2-\left(y-6\right)^2=\left(x-y+6\right)\left(x+y-6\right)\)
d) \(=y\left(x^2+4xz+4yz\right)\)
a) \(2x^2-50x\)
\(=2x\left(x-25\right)\)
b) \(x^2-5x+4\)
\(=\left(x-1\right)\left(x-4\right)\)
c) \(x^2-y^2+12y+36\)
\(=\left(x+y-6\right)\left(x-y+6\right)\)
d) \(x^2z+4xyz+4y^2z\)
\(=z\left(x^2+4xy+4y^2\right)\)
\(=z\left(x+2y\right)^2\)