Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x^2+6x-7=0\\ \Leftrightarrow x^2-x+7x-7=0\\ \Leftrightarrow x\left(x-1\right)+7\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+7=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-7\end{matrix}\right.\)
Vậy \(S=\left\{1;-7\right\}\)
\(x^2+6x-7=0\\ \Leftrightarrow x^2+7x-x-7=0\\ \Leftrightarrow\left(x^2+7x\right)-\left(x+7\right)=0\\ \Leftrightarrow x\left(x+7\right)-\left(x+7\right)=0\\ \Leftrightarrow\left(x+7\right)\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+7=0\\x-1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-7\\x=1\end{matrix}\right.\)
(x+y+z)(x+z-y)(x+y-z)(y+z-x)
=[(x+y)^2-z^2]*[(x+z-y)(y+z-x)]
=[(x+y)^2-z^2][y^2-(x+z)^2]
=(x^2+2xy+y^2-z^2][y^2-x^2-2xz-z^2]
=x^2y^2-x^4-2x^3z-x^2z^2+2xy^3-2x^3y-4x^2yz-2xyz^2+y^4-y^2x^2-2xy^2z-z^2y^2-y^2z^2+x^2z^2+2xz^3+z^4
Ta có:\(2\left(x-y\right)\left(z-y\right)+2\left(y-z\right)\left(z-x\right)+2\left(y-z\right)\left(x-z\right)\)
\(=2\left[\left(x-y\right)\left(z-y\right)+\left(y-x\right)\left(z-x\right)+\left(y-z\right)\left(x-z\right)\right]\)
\(=2\left[xz-xy-yz+y^2+yz-xy-zx+x^2+yx-yz-zx+z^2\right]\)
\(=2\left[-xz-xy-yz+x^2+y^2+z^2\right]\)
\(=x^2-2xy+y^2+y^2-2yz+z^2+z^2-2zx+x^2\)
\(=\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2\)