a) 3x² - 5x + 2 = 0
[tex]x = \frac{5 \frac{+}{} \sqrt{(-5)^2-4*3*2} }{2*3} [/tex]
[tex]x = \frac{5 \frac{+}{} \sqrt{25-24} }{6} [/tex]
[tex]x = \frac{5 \frac{+}{} \sqrt{1} }{6} [/tex]
[tex]x = \frac{5 \frac{+}{}1 }{6} [/tex]
x = (5 + 1)/6 = 6/6 = 1
x = (5 - 1)/6 = 4/6 = 2/3
Solución:
x = 1
x = 2/3
b) 4x² + 3x - 22 = 0
[tex]x = \frac{-3 \frac{+}{} \sqrt{3^2-4*4*(-22)} }{2*4}[/tex]
[tex]x = \frac{-3 \frac{+}{} \sqrt{9+352} }{8}[/tex]
[tex]x = \frac{-3 \frac{+}{} \sqrt{361} }{8}[/tex]
[tex]x = \frac{-3 \frac{+}{} 19 }{8}[/tex]
x = (-3 + 19)/8 = 16/8 = 2
x = (-3 - 19)/8 = -22/8 = -11/4
Solución:
x = 2
x = -11/4
c) x² + 11 - 24 = 0
x² - 13 = 0
x² = 13
x = √13
Solución:
x = √13
d) x(x + 3) = 5x + 3
x² + 3x = 5x + 3
x² - 2x - 3 = 0
[tex]x = \frac{2 \frac{+}{} \sqrt{(-2)^2-4*1*(-3)} }{2*1}[/tex]
[tex]x = \frac{2 \frac{+}{} \sqrt{4+12} }{2}[/tex]
[tex]x = \frac{2 \frac{+}{} \sqrt{16} }{2}[/tex]
[tex]x = \frac{2 \frac{+}{}4 }{2}[/tex]
x = (2 + 4)/2 = 6/2 = 3
x = (2 - 4)/2 = -2/2 = -1
Solución:
x = 3
x = -1
