a) \(\left(x-5\right)\left(x+3\right)-\left(x-2\right)\left(x-4\right)=1\)
\(\Leftrightarrow\left(x^2+3x-5x-15\right)-\left(x^2-4x-2x+8\right)=1\)
\(\Leftrightarrow x^2-2x-15-x^2+6x-8=1\)
\(\Leftrightarrow4x-23=1\)
\(\Leftrightarrow4x=1+23\)
\(\Leftrightarrow x=\dfrac{24}{4}\)
\(\Leftrightarrow x=6\)
b) \(\left(2x+1\right)\left(1-2x\right)+4x\left(x-5\right)=9\)
\(\Leftrightarrow\left(1+2x\right)\left(1-2x\right)+4x^2-20x=9\)
\(\Leftrightarrow\left(1-4x^2\right)+4x^2-20x=9\)
\(\Leftrightarrow1-4x^2+4x^2-20x=9\)
\(\Leftrightarrow1-20x=9\)
\(\Leftrightarrow-20x=8\)
\(\Leftrightarrow x=-\dfrac{8}{20}=-\dfrac{2}{5}\)
Bài 5
a) (x - 5)(x + 3) - (x - 2)(x - 4) = 1
x² + 3x - 5x - 15 - x² + 4x + 2x - 8 = 1
4x - 23 = 1
4x = 1 + 23
4x = 24
x = 24 : 4
x = 6
b) (2x + 1)(1 - 2x) + 4x(x - 5) = 9
1² - (2x)² + 4x² - 20x = 9
1 - 4x² + 4x² - 20x = 9
-20x = 9 - 1
-20x = 8
x = -8/20
x = -2/5
