\(x^4+5x^3+10x^2+5x-21=0\)
\(\Leftrightarrow x^4-x^3+6x^3-6x^2+16x^2-16x+21x-21=0\)
\(\Leftrightarrow x^3\left(x-1\right)+6x^2\left(x-1\right)+16x\left(x-1\right)+21\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3+6x^2+16x+21\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3+3x^2+3x^2+9x+21\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x+3\right)+3x\left(x+3\right)+9\left(x+3\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+3\right)\left(x^2+3x+9\right)=0\)
<=> x-1=0 <=> x=1
x+3=0 <=> x=-3
\(x^2+3x+9=x^2+2.\frac{3}{2}x+\frac{9}{4}+\frac{27}{4}=\left(x+\frac{3}{2}\right)^2+\frac{27}{4}>0\)
vậy nghiệm của pt là x=1; x=-3
