Ta có: \(a-b=6\) \(\Rightarrow a=b+6\)
\(\Rightarrow ab=\left(b+6\right).b=16\)
\(\Leftrightarrow b^2+6b=16\)
\(\Leftrightarrow b^2+6b-16=0\)
\(\Leftrightarrow\left(b-2\right)\left(b+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}b-2=0\\b+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}b=2\\b=-8\end{matrix}\right.\)
Mà \(a=b+6\Leftrightarrow\left[{}\begin{matrix}a=2+6=8\\a=-8+6=-2\end{matrix}\right.\)\(\)
\(\Rightarrow\left[{}\begin{matrix}a+b=8+2=10\\a+b=-2+-8=-10\end{matrix}\right.\)
Ta có: \(\left(a-b\right)^2=a^2-2ab+b^2=36\)
\(\Rightarrow a^2+b^2=36+2ab=36+2.16=68\)
\(\left(a+b\right)^2=a^2+2ab+b^2=68+2.16=100\)
\(\Rightarrow a+b=\pm10\)
Ta có : \(a-b=6\)
\(\Leftrightarrow\left(a-b\right)^2=36\)
\(\Leftrightarrow a^2-2ab+b^2=36\)
\(\Leftrightarrow a^2+b^2-2.16=36\)
\(\Leftrightarrow a^2+b^2-32=36\)
\(\Leftrightarrow a^2+b^2=68\)
\(\Leftrightarrow a^2+b^2+2ab=68+2ab\)
\(\Leftrightarrow\left(a+b\right)^2=68+2.16\)
\(\Leftrightarrow\left(a+b\right)^2=100\)
\(\Leftrightarrow\left[{}\begin{matrix}a+b=10\\a+b=-10\end{matrix}\right.\)
