Question

giải pt: \(\sqrt[3]{x+5}+\sqrt[3]{x+6}=\sqrt[3]{2x+11}\)

 

Answer 1

Lập phương hai vế : \(\left(\sqrt[3]{x+5}+\sqrt[3]{x+6}\right)^3=\left(\sqrt[3]{2x+11}\right)^3\)

\(\Leftrightarrow2x+11+3.\sqrt[3]{x+5}.\sqrt[3]{x+6}\left(\sqrt[3]{x+5}+\sqrt[3]{x+6}\right)=2x+11\)

\(\Leftrightarrow\sqrt[3]{x+5}.\sqrt[3]{x+6}\left(\sqrt[3]{x+6}+\sqrt[3]{x+5}\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}\sqrt[3]{x+5}=0\\\sqrt[3]{x+6}=0\\\sqrt[3]{x+5}+\sqrt[3]{x+6}=0\end{array}\right.\) \(\Leftrightarrow\left[\begin{array}{nghiempt}x=-5\\x=-6\\x=-\frac{11}{2}\end{array}\right.\)

Answer 2