Question

giải các phương trình
a) 3x - 12 = 2(7- x)
b) x^3 - x^2 - x + 1 = 0

Answer 1

a) \(3x-12=2\left(7-x\right)\)

\(\Leftrightarrow3x-12=14-2x\)

\(\Leftrightarrow5x=26\)

\(\Leftrightarrow x=5,2\)

b) \(x^3-x^2-x+1=0\)

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

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)