Question

giải pt:

x\(^2\)+\(\frac{8x^3}{\sqrt{9-x^2}}\)=9

Answer 1

ĐKXĐ: \(-3< x< 3\)

\(\Leftrightarrow\frac{\left(2x\right)^3}{\sqrt{9-x^2}}=9-x^2\Leftrightarrow\left(2x\right)^3=\left(9-x^2\right)\sqrt{9-x^2}\)

\(\Leftrightarrow\left(2x\right)^3=\left(\sqrt{9-x^2}\right)^3\Leftrightarrow2x=\sqrt{9-x^2}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\4x^2=9-x^2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\5x^2=9\end{matrix}\right.\) \(\Rightarrow x=\frac{3\sqrt{5}}{5}\)