Question

Giai phuong trinh

\(\sqrt{x+4}-\sqrt[3]{1-x}=1\)

Answer 1

ĐKXĐ: \(x\ge-4\)

Đặt \(\left\{{}\begin{matrix}\sqrt{x+4}=a\ge0\\\sqrt[3]{1-x}=b\end{matrix}\right.\) ta được hệ:

\(\left\{{}\begin{matrix}a-b=1\\a^2+b^3=5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=b+1\\a^2+b^3=5\end{matrix}\right.\)

\(\Rightarrow\left(b+1\right)^2+b^3=5\)

\(\Leftrightarrow b^3+b^2+2b-4=0\)

\(\Leftrightarrow\left(b-1\right)\left(b^2+2b+4\right)=0\)

\(\Leftrightarrow b=1\)

\(\Rightarrow\sqrt[3]{1-x}=1\)

\(\Rightarrow x=0\)