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d. 8x3 - 50x = 0
<=> 2x(4x - 25) = 0
<=> \(\left[{}\begin{matrix}2x=0\\4x-25=0\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=0\\x=\dfrac{25}{4}\end{matrix}\right.\)
e. (4x - 3)2 - 3x(3 - 4x) = 0
<=> (4x - 3)2 + 3x(4x - 3) = 0
<=> (4x - 3)(4x - 3 + 3x) = 0
<=> (4x - 3)(7x - 3) = 0
<=> \(\left[{}\begin{matrix}4x-3=0\\7x-3=0\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{3}{7}\end{matrix}\right.\)
d) \(8x^3-50x=0\Rightarrow2x\left(4x^2-25\right)=0\)
\(\Rightarrow2x\left(2x-5\right)\left(2x+5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x=0\\2x+5=0\\2x-5=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{5}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)
e) \(\left(4x-3\right)^2-3x\left(3-4x\right)=0\)
\(\Rightarrow\left(4x-3\right)^2+3x\left(4x-3\right)=0\)
\(\Rightarrow\left(4x-3\right)\left(4x-3+3x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}4x-3=0\\7x-3=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{3}{7}\end{matrix}\right.\)
`@` `\text {Ans}`
`\downarrow`
`a,`
`(2x - 1)^2 - 25 = 0`
`<=> (2x - 1)^2 = 25`
`<=> (2x - 1)^2 = (+-5)^2`
`<=>`\(\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Vậy, `S = {-2; 3}`
`b,`
`8x^3 - 50x = 0`
`<=> x(8x^2 - 50) = 0`
`<=>`\(\left[{}\begin{matrix}x=0\\8x^2-50=0\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x=0\\8x^2=50\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x=0\\x^2=\dfrac{25}{4}\end{matrix}\right.\)
`<=>`\(\left[{}\begin{matrix}x=0\\x=\pm\dfrac{5}{2}\end{matrix}\right.\)
Vậy, `S = {-5/2; 0; 5/2}.`
a) (2x - 1)² - 25 = 0
(2x - 1)² - 5² = 0
(2x - 1 - 5)(2x - 1 + 5) = 0
(2x - 6)(2x + 4) = 0
2x - 6 = 0 hoặc 2x + 4 = 0
*) 2x - 6 = 0
2x = 6
x = 3
*) 2x + 4 = 0
2x = -4
x = -2
Vậy x = -2; x = 3
b) 8x³ - 50x = 0
2x(4x² - 25) = 0
2x[(2x)² - 5²] = 0
2x(2x - 5)(2x + 5) = 0
2x = 0 hoặc 2x - 5 = 0 hoặc 2x + 5 = 0
*) 2x = 0
x = 0
*) 2x - 5 = 0
2x = 5
x = 5/2
*) 2x + 5 = 0
2x = -5
x = -5/2
Vậy x = -5/2; x = 0; x = 5/2
8x3-50x=0
x(8x2-50)=0
TH1: x=0 TH2: 8x2-50=0
8x2 = 50
x2 = \(\dfrac{25}{4}\)
x = + - \(\dfrac{5}{2}\)
vậy x\(\in\){0,+-\(\dfrac{5}{2}\)}