Question

Giải phương trình: \(x\sqrt{x+1}+\sqrt{3-x}-2\sqrt{x^2+1}=0\)

Answer 1

\(\left(đk:-1\le x\le3\right)\) 

\(pt\Leftrightarrow x\sqrt{x+1}+\sqrt{3-x}=2\sqrt{x^2+1}\)

\(VT\le\sqrt{\left(x^2+1\right)\left(x+1+3-x\right)}=2\sqrt{\left(x^2+1\right)}\left(bunhiacopxki\right)\)

\(\Rightarrow VT=VP\Leftrightarrow\dfrac{x}{\sqrt{x+1}}=\dfrac{1}{\sqrt{3-x}}\Leftrightarrow x\sqrt{3-x}=\sqrt{x+1}\Leftrightarrow x^2\left(3-x\right)=x+1\Leftrightarrow-\left(x-1\right)\left(x^2-2x-1\right)=0\Rightarrow x=....\)