Question

giải phương trình :  x^3- 7x + 6 = 0

Answer 1

\(x^3-7x+6=0\)

\(\Leftrightarrow x^3-x^2+x^2-x-6x+6=0\)

\(\Leftrightarrow x^2\left(x-1\right)+x\left(x-1\right)-6\left(x-1\right)=0\)

\(\Leftrightarrow\left(x^2+x-6\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left(x^2-2x+3x-6\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[x\left(x-2\right)+3\left(x-2\right)\right]\left(x-1\right)\)

\(\Leftrightarrow\left(x-2\right)\left(x+3\right)\left(x-1\right)=0\)

\(\Rightarrow x=\left\{-3;1;2\right\}\)