Question

Giải các phương trình sau:

a. 9x²(2x - 3) = 0

b. (x - 1)(3x - 6) = 0

c. (x + 2)(3 - 3x) = 0

d. \(\left(\dfrac{2}{3}x+6\right)\left(8-2x\right)=0\)

e. (4x + 2)(x² + 1) = 0

f. (3x - 4)(x + 1)(2x - 1) = 0

g. (3x - 2)²(x + 1)(x - 2) = 0

h. (2x + 3)² = (x - 5)²

Answer 1

a.

\(9x^2\left(2x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}9x^2=0\\2x-3=0\end{matrix}\right.\)

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

b.

\(\left(x-1\right)\left(3x-6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\3x-6=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

Answer 2

c.

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\)

d,

\(\left(\dfrac{2}{3}x+6\right)\left(8-2x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{3}x+6=0\\8-2x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{3}x=-6\\2x=8\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-9\\x=4\end{matrix}\right.\)

Answer 3

e,

\(\left(4x+2\right)\left(x^2+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}4x+2=0\\x^2+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}4x=-2\\x^2=-1\left(vô-nghiệm\right)\end{matrix}\right.\)

\(\Leftrightarrow x=-\dfrac{1}{2}\)

f.

\(\left(3x-4\right)\left(x+1\right)\left(2x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-4=0\\x+1=0\\2x-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=-1\\x=\dfrac{1}{2}\end{matrix}\right.\)

Answer 4

g.

\(\left(3x-2\right)^2\left(x+1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(3x-2\right)^2=0\\x+1=0\\x-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-2=0\\x=-1\\x=2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-1\\x=2\end{matrix}\right.\)

h.

\(\left(2x+3\right)^2=\left(x-5\right)^2\)

\(\Leftrightarrow\left(2x+3\right)^2-\left(x-5\right)^2=0\)

\(\Leftrightarrow\left(3x-2\right)\left(x+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-2=0\\x+8=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-8\end{matrix}\right.\)