Question

Giải các phương trình sau ( đặt biến phụ)

1, 2x³ + 7x² + 7x + 2 =0

2, x⁵+2x⁴+ 3x³+3x² + 2x +1=0

3,x⁴-3x³+4x²-3x+1=0

Answer 1

\(2x^3+7x^2+7x+2=0\)

\(\Leftrightarrow\left(2x^3+7x^2+7x\right)+2=0\)

\(\Leftrightarrow x\left(2x^2+7x+7+2\right)=0\)

\(\Leftrightarrow x\left(2x^2+7x+9\right)=0\)

\(\Leftrightarrow x\left(2x^2+6x+3x+9\right)=0\)

\(\Leftrightarrow x\left[\left(2x^2+6x\right)+\left(3x+9\right)\right]=0\)

\(\Leftrightarrow x\left[2x\left(x+3\right)+3\left(x+3\right)\right]=0\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x+3=0\\2x+3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=-3\\x=-\dfrac{3}{2}\end{matrix}\right.\)

chúc bạn học tốt!