Đáp án + Giải thích các bước giải:
a. `3x^2 - x = 0`
`⇒ x(3x - 1) = 0`
`=>` \(\left[ \begin{array}{l}x=0\\3x-1=0\end{array} \right.\) `=>` \(\left[ \begin{array}{l}x=0\\x=\dfrac{1}{3}\end{array} \right.\)
Vậy `x ∈ {0; 1/3}`
b. `4x^3 - 4x = 0`
`=> 4x(x^2 - 1) = 0`
`=> 4x(x-1)(x+1) =0`
`=>` \(\left[ \begin{array}{l}4x=0\\x-1=0\\x+1=0\end{array} \right.\) `=>` \(\left[ \begin{array}{l}x=0\\x=±1\end{array} \right.\)
Vậy `x ∈{0; ±1}`
c. `5x(x-1) = x-1`
`⇒ 5x(x-1) - (x-1) = 0`
`=> (x-1)(5x-1) = 0`
`=>` \(\left[ \begin{array}{l}x-1=0\\5x-1=0\end{array} \right.\) `=>` \(\left[ \begin{array}{l}x=1\\x=\dfrac{1}{5}\end{array} \right.\)
Vậy `x ∈{1; 1/5}`
d. `2(x+5) = x^2 + 5x`
`=> 2(x+5) = x(x + 5)`
`=> x(x+5) - 2(x+5) = 0`
`=> (x+5)(x-2) = 0`
`=>` \(\left[ \begin{array}{l}x+5=0\\x-2=0\end{array} \right.\) `=>` \(\left[ \begin{array}{l}x=-5\\x=2\end{array} \right.\)
Vậy `x ∈ {-5; 2}`
