Question

x⁴ - 2x³-x²+8x-12=0

Answer 1

\(\Leftrightarrow x^4-2x^3-\left(x^2-2x\right)+\left(6x-12\right)=0\Leftrightarrow x^3\left(x-2\right)-x\left(x-2\right)+6\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-x+6\right)=0\Leftrightarrow\left(x-2\right)\left(x^3+2x^2-\left(2x^2+4x\right)+\left(3x+6\right)\right)=0\)

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

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

( vì X² -2X +3 =(X -1 )² +1 >0)