Question

Giải phương trình x³ -12x - 16 =0

Answer 1

Nguyễn TrươngTruong Viet TruongAkai HarumaMysterious PersonMashiro Shiina

Answer 2

PT<=>x³-12x-16=0<=>x³-64-12x+48=0

<=>(x-4)(x²+4x+16)-12(x-4)=0 <=> (x-4)(x²+4x+4)=0

<=>(x-4)(x+2)²=0<=> \(\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)

Answer 3

\(x^3-12x-16=0\\ \Leftrightarrow x^3-16x+4x-16=0\\ \Leftrightarrow x\left(x^2-16\right)+4\left(x-4\right)=0\\ \Leftrightarrow x\left(x-4\right)\left(x+4\right)+4\left(x-4\right)=0\\ \Leftrightarrow\left(x-4\right)\left[x\left(x+4\right)+4\right]=0\\ \Leftrightarrow\left(x-4\right)\left(x^2+4x+4\right)=0\\ \Leftrightarrow\left(x-4\right)\left(x+2\right)^2=0\\ \Leftrightarrow\left[{}\begin{matrix}x-4=0\\\left(x+2\right)^2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)