a)\(2x^3+3x^2+2x+3=0\)
\(\Leftrightarrow2x^3+2x+3x^2+3=0\)
\(\Leftrightarrow2x\left(x^2+1\right)+3\left(x^2+1\right)=0\)
\(\Leftrightarrow\left(2x+3\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}2x+3=0\\x^2+1=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}2x=-3\\x^2+1>0\left(loai\right)\end{array}\right.\)
\(\Leftrightarrow x=-\frac{3}{2}\)
b)\(x\left(2x-1\right)\left(1-2x\right)=0\)
\(\Leftrightarrow-x\left(2x-1\right)\left(2x-1\right)=0\)
\(\Leftrightarrow-x\left(2x-1\right)^2=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}-x=0\\\left(2x-1\right)^2=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\2x=1\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=\frac{1}{2}\end{array}\right.\)
\(2x^3+3x^2+2x+3=0\)
\(2x\left(x^2+1\right)+3\left(x^2+1\right)=0\)
\(\left(2x+3\right)\left(x^2+1\right)=0\)
\(2x+3=0\left(x^2+1\ge1>0\right)\)
\(2x=-3\)
\(x=-\frac{3}{2}\)
\(x\left(2x-1\right)\left(1-2x\right)=0\)
\(\left[\begin{array}{nghiempt}x=0\\2x-1=0\\1-2x=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=0\\2x=1\\2x=1\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=0\\x=\frac{1}{2}\end{array}\right.\)
a)2x3+3x2+2x+3=0
(2x3+2x)+(3x2+3)=0
2x(x2+1)+3(x2+1)=0
(x2+1)(2x+3)=0
Vì x luôn luôn lớn hơn hoặc bằng 0 (với mọi x). Nên x+1>0 (với mọi x)
→ 2x+3=0
->x=-3/2
Vậy x=-3/2
b)x(2x-1)(1-2x)=0
=>x=0
=> 2x-1=0 => x=1/2
=>1-2x=0 => x=1/2
Vậy x=0 hoặc x=1/2.
