\(\Leftrightarrow\) \(\sqrt{\left(x+2\right)^2}\) + \(\left|x-4\right|=0\) ( ĐKXĐ : \(\left(x+2\right)^2\ge0\) luôn đúng \(\forall x\) )
\(\Leftrightarrow\) x + 2 + \(\left|x-4\right|\) = 0 (*)
TH1 : x \(\ge4\) \(\Leftrightarrow\) \(\left|x-4\right|=x-4\) TH2 : x < 4 \(\Leftrightarrow\) \(\left|x-4\right|=-x+4\)
\(\Rightarrow\) (*) = x + 2 + x - 4 = 0 \(\Rightarrow\) (*) = x + 2 - x + 4 = 0
\(\Leftrightarrow\) 2x - 2 = 0 \(\Leftrightarrow\) 6 = 0 ( vô lí )
\(\Leftrightarrow\) x = 1 (KTM) (1) \(\Leftrightarrow\) \(x\in\varnothing\) (2)
Từ (1) và (2) \(\Rightarrow\) \(x\in\varnothing\)
