Đáp án+Giải thích các bước giải:
`a) (x-3)(x-1)-x(x-2)=0`
`⇔ x^2 - x - 3x + 3 - x^2 + 2x = 0`
`⇔ -2x + 3 = 0`
`⇔ -2x = -3`
`⇔ x = 3/2`
Vậy `S = {3/2}`
`b) (2x-3)^2 - 4(x-1)(x+1)=13`
`⇔ 4x^2 - 12x + 9 - 4(x^2-1) - 13 = 0`
`⇔ 4x^2 -12x - 4 - 4x^2 + 4 = 0`
`⇔ -12x = 0`
`⇔ x = 0`
Vậy `S = {0}`
`c) x^2 - 4x - 2 = 0`
`⇔ x^2 - 2.x.2 + 2^2 - 2^2 - 2 = 0`
`⇔ (x-2)^2 - 6 = 0`
`⇔ (x-2)^2 = 6`
⇔\(\left[ \begin{array}{l}x-2=\sqrt{6}\\x-2=-\sqrt{6}\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=\sqrt{6}+2\\x=-\sqrt{6}+2\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=2+\sqrt{6}\\x=2-\sqrt{6}\end{array} \right.\)
Vậy `S = {2+\sqrt{6}; 2-\sqrt{6}}`
`d) (6x-5)^2 = 4(7-5x)^2`
`⇔ 36x^2 - 60x + 25 = 4(49 - 70x + 25x^2)`
`⇔ 36x^2 - 60x + 25 - 4(49 - 70x + 25x^2) = 0`
`⇔ 36x^2 - 60x + 25 - 196 + 280x - 100x^2 = 0`
`⇔ -64x^2 + 220x - 171 = 0`
`⇔ -64x^2 + 144x + 76x - 171 = 0`
`⇔ -64x(x - 9/4) + 76(x - 9/4) = 0`
`⇔ (x-9/4)(-64x+76) = 0`
⇔\(\left[ \begin{array}{l}x-\dfrac{9}{4}=0\\-64x+76=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=\dfrac{9}{4}\\-64x=-76\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=\dfrac{9}{4}\\x=\dfrac{19}{16}\end{array} \right.\)
Vậy `S = {9/4; 19/16}`
