dkxd: -2 ≤ x ≤ 2
\(x+\sqrt{4-x^2}=2+3x\sqrt{4-x^2}\)
\(\Leftrightarrow x-2=3x\sqrt{4-x^2}-\sqrt{4-x^2}\)
\(\Leftrightarrow x-2=\sqrt{4-x^2}\left(3x-1\right)\)
\(\Leftrightarrow x^2-4x+4=\left(4-x^2\right)\left(9x^2-6x+1\right)\)
\(\Leftrightarrow x^2-4x+4=-9x^4+6x^3+35x^2-24x+4\)
\(\Leftrightarrow9x^4-6x^3-34x^2+20x=0\)
\(\Leftrightarrow x\left(9x^3-6x^2-34x+20\right)=0\)
\(\Leftrightarrow x\left(x-2\right)\left(9x^2+12x-10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-2=0\\9x^2+12x-10=0\end{matrix}\right.\)
+) => x= 0 (nhận)
+) x - 2 = 0 => x = 2 (nhận)
+) \(9x^2+12x-10=0\)
\(\Leftrightarrow\left(9x^2+12x+4\right)-14=0\)
\(\Leftrightarrow\left(3x+2\right)^2=14\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+2=\sqrt{14}\\3x+2=-\sqrt{14}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-2+\sqrt{14}}{3}\left(loai\right)\\x=\dfrac{-2-\sqrt{14}}{3}\left(nhan\right)\end{matrix}\right.\)
Vậy pt có 3 nghiệm ...........
