Question

Giai pt: \(\sqrt{\left(x^2+2\right)^2}=x^2+2x+5\)

Answer 1

=>|x^2+2|=x^2+2x+5

=>x^2+2=x^2+2x+5(Do x^2+2>=2>0 với mọi x)

=>2x+5=2

=>2x=-3

=>x=-3/2

Answer 2

\(\sqrt{\left(x^2+2\right)^2}=x^2+2x+5\)

\(\Leftrightarrow\left|x^2+2\right|=x^2+2x+5\)  

Mà: \(x^2+2\ge2>0\forall x\)

\(\Leftrightarrow x^2+2=x^2+2x+5\)

\(\Leftrightarrow x^2-x^2+2x+5-2=0\)

\(\Leftrightarrow2x+3=0\)

\(\Leftrightarrow2x=-3\)

\(\Leftrightarrow x=-\dfrac{3}{2}\)