Dưới đây là lời giải cho các phương trình trong bài tập:

a) \( x^2 - 9 = 0 \)
\[ x^2 = 9 \]
\[ x = \pm 3 \]

b) \( 4x^2 - 4 = 0 \)
\[ 4x^2 = 4 \]
\[ x^2 = 1 \]
\[ x = \pm 1 \]

c) \( 4x^2 - 36 = 0 \)
\[ 4x^2 = 36 \]
\[ x^2 = 9 \]
\[ x = \pm 3 \]

d) \( (5x - 4)^2 - 49x^2 = 0 \)
\[ 25x^2 - 40x + 16 - 49x^2 = 0 \]
\[ -24x^2 - 40x + 16 = 0 \]
\[ 24x^2 + 40x - 16 = 0 \]
\[ 3x^2 + \frac{5}{3}x - \frac{2}{3} = 0 \]
\[ x = -\frac{5}{6} \pm \frac{\sqrt{(5/6)^2 + 4 \cdot 3 \cdot 2/3}}{2 \cdot 3} \]

e) \( (3x - 5) - (x + 1) = 0 \)
\[ 3x - 5 - x - 1 = 0 \]
\[ 2x - 6 = 0 \]
\[ x = 3 \]

f) \( (2x + 1) - (x - 1) = 0 \)
\[ 2x + 1 - x + 1 = 0 \]
\[ x + 2 = 0 \]
\[ x = -2 \]

g) \( (3x - 1) - (x + 5) = 0 \)
\[ 3x - 1 - x - 5 = 0 \]
\[ 2x - 6 = 0 \]
\[ x = 3 \]

h) \( (2x - 3) - (x + 5) = 0 \)
\[ 2x - 3 - x - 5 = 0 \]
\[ x - 8 = 0 \]
\[ x = 8 \]

i) \( (3x - 4) - (x + 2) = 0 \)
\[ 3x - 4 - x - 2 = 0 \]
\[ 2x - 6 = 0 \]
\[ x = 3 \]

j) \( x(x + 1) - x^2 + 1 = 0 \)
\[ x^2 + x - x^2 + 1 = 0 \]
\[ x + 1 = 0 \]
\[ x = -1 \]

k) \( 4x(x - 2) - 6 + 3x = 0 \)
\[ 4x^2 - 8x - 6 + 3x = 0 \]
\[ 4x^2 - 5x - 6 = 0 \]
\[ x = \frac{5 \pm \sqrt{25 + 96}}{8} \]
\[ x = \frac{5 \pm 11}{8} \]
\[ x = 2 \text{ or } x = -\frac{3}{4} \]

l) \( x(x + 2) - 3(x + 2) = 0 \)
\[ x(x + 2) - 3(x + 2) = 0 \]
\[ (x - 3)(x + 2) = 0 \]
\[ x = 3 \text{ or } x = -2 \]

m) \( 8x(x - 5) - 2x + 10 = 0 \)
\[ 8x^2 - 40x - 2x + 10 = 0 \]
\[ 8x^2 - 42x + 10 = 0 \]
\[ x = \frac{42 \pm \sqrt{1764 - 320}}{16} \]
\[ x = \frac{42 \pm \sqrt{1444}}{16} \]
\[ x = \frac{42 \pm 38}{16} \]
\[ x = 5 \text{ or } x = \frac{1}{4} \]

n) \( x(2x - 3) - 2(3 - 2x) = 0 \)
\[ 2x^2 - 3x - 6 + 4x = 0 \]
\[ 2x^2 + x - 6 = 0 \]
\[ x = \frac{-1 \pm \sqrt{1 + 48}}{4} \]
\[ x = \frac{-1 \pm 7}{4} \]
\[ x = 1.5 \text{ or } x = -2 \]

o) \( (x - 1)^2 + x(4 - x) = 11 \)
\[ x^2 - 2x + 1 + 4x - x^2 = 11 \]
\[ 2x + 1 = 11 \]
\[ 2x = 10 \]
\[ x = 5 \]

p) \( (x - 5)^2 - x(x + 2) = 5 \)
\[ x^2 - 10x + 25 - x^2 - 2x = 5 \]
\[ -12x + 25 = 5 \]
\[ -12x = -20 \]
\[ x = \frac{5}{3} \]

q) \( x(x + 4) - x - 6x = 10 \)
\[ x^2 + 4x - x - 6x = 10 \]
\[ x^2 - 3x = 10 \]
\[ x^2 - 3x - 10 = 0 \]
\[ x = \frac{3 \pm \sqrt{9 + 40}}{2} \]
\[ x = \frac{3 \pm 7}{2} \]
\[ x = 5 \text{ or } x = -2 \]

r) \( 2(x + 3) - x - 3x = 0 \)
\[ 2x + 6 - x - 3x = 0 \]
\[ -2x + 6 = 0 \]
\[ x = 3 \]

s) \( 3x(x - 5) - x + 25 = 0 \)
\[ 3x^2 - 15x - x + 25 = 0 \]
\[ 3x^2 - 16x + 25 = 0 \]
\[ x = \frac{16 \pm \sqrt{256 - 300}}{6} \]
\[ x = \frac{16 \pm \sqrt{-44}}{6} \]
\[ \text{No real solution} \]

t) \( 3x(2x - 1) - 24x + 12 = 0 \)
\[ 6x^2 - 3x - 24x + 12 = 0 \]
\[ 6x^2 - 27x + 12 = 0 \]
\[ x = \frac{27 \pm \sqrt{729 - 288}}{12} \]
\[ x = \frac{27 \pm \sqrt{441}}{12} \]
\[ x = \frac{27 \pm 21}{12} \]
\[ x = 4 \text{ or } x = \frac{1}{2} \]

u) \( x(x - 2019) - x + 2019 = 0 \)
\[ x^2 - 2019x - x + 2019 = 0 \]
\[ x^2 - 2020x + 2019 = 0 \]
\[ x = \frac{2020 \pm \sqrt{4080400 - 8076}}{2} \]
\[ x = \frac{2020 \pm \sqrt{4072324}}{2} \]
\[ x = \frac{2020 \pm 2018}{2} \]
\[ x = 2019 \text{ or } x = 1 \]

v) \( 3x(x - 2019) - x + 2019 = 0 \)
\[ 3x^2 - 6057x - x + 2019 = 0 \]
\[ 3x^2 - 6058x + 2019 = 0 \]
\[ x = \frac{6058 \pm \sqrt{36700864 - 24228}}{6} \]
\[ x = \frac{6058 \pm \sqrt{36676636}}{6} \]
\[ x = \frac{6058 \pm 6056}{6} \]
\[ x = 2019 \text{ or } x = \frac{1}{3} \]

w) \( (x + 2) - (x - 2)(x + 2) = 0 \)
\[ x + 2 - (x^2 - 4) = 0 \]
\[ x + 2 - x^2 + 4 = 0 \]
\[ -x^2 + x + 6 = 0 \]
\[ x = \frac{-1 \pm \sqrt{1 + 24}}{2} \]
\[ x = \frac{-1 \pm 5}{2} \]
\[ x = 2 \text{ or } x = -3 \]

x) \( (x + 3) - (x + 2)(x - 2) = 4x + 17 \)
\[ x + 3 - (x^2 - 4) = 4x + 17 \]
\[ x + 3 - x^2 + 4 = 4x + 17 \]
\[ -x^2 - 3x - 10 = 0 \]
\[ x = \frac{-3 \pm \sqrt{9 + 40}}{2} \]
\[ x = \frac{-3 \pm 7}{2} \]
\[ x = 2 \text{ or } x = -5 \]

y) \( (2x + 1) - (4x - 1)(x - 3) - 15 = 0 \)
\[ 2x + 1 - (4x^2 - 13x + 3) - 15 = 0 \]
\[ 2x + 1 - 4x^2 + 13x - 3 - 15 = 0 \]
\[ -4x^2 + 15x - 17 = 0 \]
\[ x = \frac{15 \pm \sqrt{225 + 272}}{8} \]
\[ x = \frac{15 \pm 19}{8} \]
\[ x = 4.25 \text{ or } x = -0.5 \]

z) \( (2x + 3)(x - 1) + (2x - 3)(1 - x) = 0 \)
\[ 2x^2 + x - 3 + 2x - 3 = 0 \]
\[ 2x^2 + 3x - 6 = 0 \]
\[ x = \frac{-3 \pm \sqrt{9 + 48}}{4} \]
\[ x = \frac{-3 \pm 7}{4} \]
\[ x = 1 \text{ or } x = -2.5 \]

aa) \( 2(5x - 8) - 3(4x - 5) = 4(3x - 4) + 11 \)
\[ 10x - 16 - 12x + 15 = 12x - 16 + 11 \]
\[ -2x - 1 = 12x - 5 \]
\[ -2x - 12x = -5 + 1 \]
\[ -14x = -4 \]
\[ x = \frac{2}{7} \]

bb) \( (3x - 1)(2x - 7) - (1 - 3x)(6x - 5) = 0 \)
\[ 6x^2 - 21x - 2x + 7 - 6x + 15x = 0 \]
\[ 6x^2 - 14x + 7 = 0 \]
\[ x = \frac{14 \pm \sqrt{196 - 168}}{12} \]
\[ x = \frac{14 \pm 4}{12} \]
\[ x = 1.5 \text{ or } x = 0.833 \]

Hy vọng các lời giải trên sẽ giúp bạn hiểu rõ hơn về cách giải các phương trình này.