b) 5x2 - 20x = 0
\(\Leftrightarrow\) 5x(x - 4) = 0
Khi 5x = 0 hoặc x - 4 = 0
\(\Leftrightarrow\) x = \(\dfrac{0}{5}\) \(\Leftrightarrow\) x = 4
\(\Leftrightarrow\) x = 0
Vậy S = \(\left\{0;4\right\}\)
c) 7x(2x - 6) - 3(2x - 6) = 0
\(\Leftrightarrow\) (2x - 6)(7x - 3) = 0
Khi 2x - 6 = 0 hoặc 7x - 3 = 0
\(\Leftrightarrow\) 2x = 6 \(\Leftrightarrow\) 7x = 3
\(\Leftrightarrow\) x = \(\dfrac{6}{2}=3\) \(\Leftrightarrow\) x = \(\dfrac{3}{7}\)
Vậy S = \(\left\{3;\dfrac{3}{7}\right\}\)
d) (2x - 3)(x + 2) = (2x - 3)(5 - 3x)
\(\Leftrightarrow\) (2x - 3)(x + 2) - (2x - 3)(5 - 3x) = 0
\(\Leftrightarrow\) (2x - 3)\(\left[\left(x+2\right)-\left(5-3x\right)\right]\) = 0
\(\Leftrightarrow\) (2x - 3)(x + 2 - 5 + 3x) = 0
\(\Leftrightarrow\) (2x - 3)(4x - 3) = 0
khi 2x - 3 = 0 hoặc 4x - 3 = 0
\(\Leftrightarrow\) 2x = 3 \(\Leftrightarrow\) 4x = 3
\(\Leftrightarrow\) x = \(\dfrac{3}{2}\) \(\Leftrightarrow\) x = \(\dfrac{3}{4}\)
Vậy S = \(\left\{\dfrac{3}{2};\dfrac{3}{4}\right\}\)
e) 3x(x - 2) = 2x - 4
\(\Leftrightarrow\) 3x(x - 2) = 2(x - 2)
\(\Leftrightarrow\) 3x(x - 2) - 2(x - 2) = 0
\(\Leftrightarrow\) (x - 2)(3x - 2) = 0
Khi x - 2 = 0 hoặc 3x - 2 = 0
\(\Leftrightarrow\) x = 2 \(\Leftrightarrow\) 3x = 2
\(\Leftrightarrow\) x = \(\dfrac{2}{3}\)
Vậy S = \(\left\{2;\dfrac{2}{3}\right\}\)
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Mình bổ sung :
f) (x + 1)2 = (x + 1)
\(\Leftrightarrow\) (x + 1)2 - (x + 1) = 0
\(\Leftrightarrow\) (x + 1)(x + 1 - 1) = 0
\(\Leftrightarrow\) (x + 1) .x = 0
Khi x = 0 hoặc x + 1= 0
\(\Leftrightarrow\) x = -1
g) 3x(x - 2020) - x + 2020 = 0
\(\Leftrightarrow\) 3x(x - 2020) - (x - 2020) = 0
\(\Leftrightarrow\) (x - 2020)(3x - 1) = 0
Khi x - 2020 = 0 hoặc 3x - 1 = 0
\(\Leftrightarrow\) x = 2020 \(\Leftrightarrow\) 3x = 1
\(\Leftrightarrow\) x = \(\dfrac{1}{3}\)
Vậy S = \(\left\{2020;\dfrac{1}{3}\right\}\)
h) 2x(x - 2) - 6x + 12 = 0
\(\Leftrightarrow\) 2x(x - 2) - 6(x - 2) = 0
\(\Leftrightarrow\) (x - 2)(2x - 6) = 0
Khi x - 2 = 0 hoặc 2x - 6 = 0
\(\Leftrightarrow\) x = 2 \(\Leftrightarrow\) 2x = 6
\(\Leftrightarrow\) x = \(\dfrac{6}{2}=3\)
Vậy S = \(\left\{2;3\right\}\)
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