a: \(a-b=6\)
=>\(\left(a-b\right)^2=6^2=36\)
=>\(a^2+b^2-2ab=36\)
=>\(a^2+b^2=36+2ab=36+2\cdot2=40\)
\(\left(a+b\right)^2=a^2+b^2+2ab=40+2\cdot2=44\)
=>\(\left[{}\begin{matrix}a+b=2\sqrt{11}\\a+b=-2\sqrt{11}\end{matrix}\right.\)
\(M=\left(a+1\right)^2+\left(b+1\right)^2\)
\(=a^2+2a+1+b^2+2b+1\)
\(=\left(a^2+b^2\right)+2\left(a+b\right)+2\)
\(=40+2+2\left(a+b\right)\)
\(=42+2\left(a+b\right)=\left[{}\begin{matrix}42+2\cdot2\sqrt{11}=42+4\sqrt{11}\\42+2\cdot\left(-2\sqrt{11}\right)=42-4\sqrt{11}\end{matrix}\right.\)
b: \(x^2-4x+6=\dfrac{21}{x^2-4x+10}\)
=>\(\left(x^2-4x+6\right)\left(x^2-4x+10\right)=21\)
=>\(\left(x^2-4x\right)^2+16\left(x^2-4x\right)+60-21=0\)
=>\(\left(x^2-4x\right)^2+16\left(x^2-4x\right)+39=0\)
=>\(\left(x^2-4x+13\right)\left(x^2-4x+3\right)=0\)
mà \(x^2-4x+13=\left(x-2\right)^2+9>=9>0\forall x\)
nên \(x^2-4x+3=0\)
=>(x-1)(x-3)=0
=>\(\left[{}\begin{matrix}x-1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
