Giải thích các bước giải:
$a) 3x.(x -10) = x -10$
$⇔ 3x.(x -10) -(x -10) = 0$
$⇔ (x -10).(3x -1) = 0$
$⇔ \left[ \begin{array}{l}x -10=0\\3x -1=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=10\\x=1/3\end{array} \right.$
Vậy` S = {10; 1/3}`
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$b) x² +6x +5 = 0$
$⇔ x.(x +1) +5.(x +1) = 0$
$⇔ (x +1).(x +5) = 0$
$⇔ \left[ \begin{array}{l}x +1=0\\x +5=0\end{array} \right. ⇔ \left[ \begin{array}{l}x=-1\\x=-5\end{array} \right.$
Vậy `S = {-1; -5}`
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$c) x² -9 +2.(x -3)² = 10$
$⇔ x² -9 +2x² -12x +18 -10 = 0$
$⇔ 3x² -12x -1 = 0$
`⇔ 3.(x² -4x -1/3) = 0`
`⇔ 3.[(x)² -2.x.2 +(2)² -(2)² -1/3] = 0`
`⇔ 3.[(x -2)² -13/3] = 0`
$⇔ 3.(x -2 -\sqrt{\dfrac{13}{3}}).(x -2 +\sqrt{\dfrac{13}{3}}) = 0$
$⇔ \left[ \begin{array}{l}x -2 -\sqrt{\dfrac{13}{3}} = 0\\x -2 +\sqrt{\dfrac{13}{3}}=0\end{array} \right. $ $⇔ \left[ \begin{array}{l}x=\dfrac{6 +\sqrt{39}}{3}\\x=\dfrac{6 -\sqrt{39}}{3}\end{array} \right.$
Vậy `S = {`$\dfrac{6 +\sqrt{39}}{3}; \dfrac{6 -\sqrt{39}}{3}$`}`
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$d) 3.(x +4) -2x.(4 -x) = 0$
$⇔ 3x +12 -8x +2x² = 0$
$⇔ 2x² -5x +12 = 0$
`⇔ 2.(x² -5/2x +6) = 0`
`⇔ 2.[(x -5/4)² +71/16] = 0`
`⇔ 2.(x -5/4)² +71/8 = 0` (Vô lý)
Vì `2.(x -5/4)² +71/8 > 0` (vs ∀ x)
Vậy `S = ∅`
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$e) (x +5)² -x(x +8) = 3$
$⇔ x² +10x +25 -x² -8x = 3$
$⇔ 2x = -22$
$⇔ x = -11$
Vậy `S = {-11}`
