Question

Tìm x biết:

3x^2 + x = 6

Phương pháp tách hạng tử

Answer 1

\(3x^2+x=6\)

\(\Leftrightarrow3x^2+x-6=0\)

\(\Leftrightarrow3\left(x^2+\dfrac{1}{3}x+\dfrac{1}{36}\right)-\dfrac{73}{12}=0\)

\(\Leftrightarrow3\left(x+\dfrac{1}{6}\right)^3=\dfrac{73}{12}\)

\(\Rightarrow\left(x+\dfrac{1}{6}\right)^2=\dfrac{73}{36}\)

\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{6}=\sqrt{\dfrac{73}{36}}\\x+\dfrac{1}{6}=-\sqrt{\dfrac{73}{36}}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{73}{36}}-\dfrac{1}{6}\\x=-\sqrt{\dfrac{73}{36}}-\dfrac{1}{6}\end{matrix}\right.\)