Question

\(\text{Giải phương trình:}\\\sqrt{x^2+x+1}+\sqrt{x^2-x+1}=\sqrt{2x^2+4}\)

Answer 1

\(\Leftrightarrow2x^2+2+2\sqrt{\left(x^2+x+1\right)\left(x^2-x+1\right)}=2x^2+4\)

\(\Leftrightarrow\sqrt{x^4+x^2+1}=1\)

\(\Leftrightarrow x^4+x^2=0\)

\(\Leftrightarrow x=0\)

Answer 2

`\sqrt{x^2+x+1}+\sqrt{x^2-x+1}=\sqrt{2x^2+4}`

`<=>2x^2+2+2\sqrt{x^4+x^2+1}=2x^2+3`

`<=>\sqrt{x^4+x^2+1}=1`

`<=>x^4+x^2=0`

`<=>x=0`