\(\left(x-3\right)^{x+3}-\left(x-3\right)^{x+1}=0\)

\(\left(x-3\right)^{x+1}\left[\left(x-3\right)^2-1\right]=0\)

\(\left(x-3\right)^{x+1}\left(x^2-6x+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x^2-6x+8=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=4\\x=2\end{matrix}\right.\)

Vậy \(S=\left\{2;3;4\right\}\)

\(\sqrt{x+2}+\sqrt{9x+18}=\sqrt{4x+8+6}\)

\(\sqrt{x+2}+\sqrt{9\left(x+2\right)}=\sqrt{4x+14}\) \(\left(Đk:x\ge-2\right)\)

\(4\sqrt{x+2}=\sqrt{4x+14}\)

\(16\left(x+2\right)=4x+14\)

\(12x=-18\)

\(x=-\dfrac{3}{2}\left(TM\right)\)

Vậy \(S=\left\{-\dfrac{3}{2}\right\}\)

\(44.102\)

\(=44.\left(100+2\right)\)

\(=44.100+44.2\)

\(=4400+88\)

\(=4488\)

\(x+y+z=0\)

\(\Rightarrow x+y=-z\)

\(\Rightarrow x^2+y^2-z^2=-2xy\)

Tương tự: \(\left\{{}\begin{matrix}y^2+z^2-x^2=-2yz\\z^2+x^2-y^2=-2zx\end{matrix}\right.\)

\(A=\dfrac{xy}{x^2+y^2-z^2}+\dfrac{yz}{y^2+z^2-x^2}+\dfrac{zx}{z^2+x^2-y^2}\)

\(=-\left(\dfrac{xy}{2xy}+\dfrac{yz}{2yz}+\dfrac{zx}{2zx}\right)=-\dfrac{3}{2}\)

\(\left(x-\dfrac{1}{2}\right)^3=81=\left(\sqrt[3]{81}\right)^3\)

\(\Leftrightarrow x-\dfrac{1}{2}=\sqrt[3]{81}\)

\(\Leftrightarrow x=\sqrt[3]{81}+\dfrac{1}{2}\)

\(x^3+y^3+21x+21y\)

\(=\left(x+y\right)\left(x^2-xy+y^2\right)+21\left(x+y\right)\)

\(=\left(x+y\right)\left(x^2-xy+y^2+21\right)\)