Đáp án + Giải thích các bước giải:
12)
$x² + 3(x² - 1) = x(4x + 1)$
$x² + 3x² - 3 = 4x² + x$
$4x² - 4x² + x = -3$
$x = -3$
13)
$3x(x+1) - 2x(x + 2) = 4-x$
$3x² + 3x - 2x² - 4x = 4-x$
$x² - x + x = 4$
$x² = 4$
$x = ±2$
14)
$(x-3)(x + 7) - (x+5)(x-1) = 0$
$x² + 4x - 21 - x² - 4x + 5 = 0$
$16 = 0$
pt vô nghiệm
15)
$(2x-1)² - 16 = 0$
$(2x-1)² = 16$
$(2x-1)² = ±4²$
\(\left[ \begin{array}{l}x=\dfrac{5}{2}\\x=\dfrac{-3}{2}\end{array} \right.\)
16)
$x² - x + \dfrac{1}{4} = 9$
$x² - 2.x.\dfrac{1}{2} + (\dfrac{1}{2})² = 9$
$(x-\dfrac{1}{2})² = 3²$
\(\left[ \begin{array}{l}x=\dfrac{5}{2}\\x=\dfrac{-7}{2}\end{array} \right.\)
17)
$(2x+1)² - 4(x+2)² = 11$
$4x² + 4x + 1 - 4(x² + 4x + 4) = 11$
$4x² + 4x + 1 - 4x² - 16x - 16 = 11$
$-12x - 15 = 11$
$-12x = 26$
$x = \dfrac{-13}{6}$
18)
$(x+1)³ - (x-1)³ - 6(x-1)² = -1$
$x³ + 3x² + 3x + 1 - x³ + 3x² - 3x + 1 - 6(x² - 2x + 1) = -1$
$6x² + 2 - 6x² + 12x - 6 = -1$
$12x - 4 = -1$
$12x = 3$
$x = \dfrac{1}{4}$
19)
$(x-1)² - x(x-5) = 3$
$x² - 2x + 1 - x² + 5x = 3$
$3x + 1 = 3$
$3x = 2
$x = \dfrac{2}{3}$
