Question

Giải phương trình x² - 4x + 4 = \(\sqrt{-3x+6}\)

Answer 1

\(\text{ĐKXĐ: }-3x+6\ge0\)

\(\Leftrightarrow-3x\ge-6\)

\(\Leftrightarrow x\le2\)

\(x^2-4x+4=\sqrt{-3x+6}\)

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

\(\Leftrightarrow\left(x-2\right)^4=-3.\left(x-2\right)\)

\(\Leftrightarrow\left(x-2\right)^3=-3\)

\(\Leftrightarrow\left(x-2\right)^3=\left(\sqrt[3]{-3}\right)^3\)

\(\Leftrightarrow x-2=\sqrt[3]{-3}\)

\(\Leftrightarrow x=\sqrt[3]{-3}+2\)\(\left(\text{thỏa mãn}\right)\)

\(\text{Vậy }x=\sqrt[3]{-3}+2\)