Question

Determine os valores de x nas equações do segundo grau abaixo: 3x² = 18x b) (x + 2) . (x – 2) = 20

Answer 1

Resposta:

a)  3x² = 18x

$x_{1} =\frac{(-18)+18}{2.3} = \frac{0}{6} = 0 \\x_{2} =\frac{(-18)-18}{2.3} = \frac{-36}{6} = -6$

b) (x + 2) . (x – 2) = 20

$x_{1} = \frac{0 + 9,8}{2.1} = \frac{9,8}{2} = 4,9\\x_{2} = \frac{0 - 9,8 }{2*1} = \frac{-9,8}{2} = -4,9$

Explicação passo a passo:

a)  3x² = 18x

3x² -18x =0

Δ=$b^{2} - 4.a.c$

$(-18)^{2} - 4.3.0 \\ 324 - 0$

Δ= 324

x'= -b ±√Δ / 2.a

$x_{1} =\frac{(-18)+18}{2.3} = \frac{0}{6} = 0 \\x_{2} =\frac{(-18)-18}{2.3} = \frac{-36}{6} = -6$

b) (x + 2) . (x – 2) = 20

$x^{2} -2x +2x -4 = 20 \\x^{2} -4 = 20 \\x^{2} -4 -20 = 0\\x^{2} -24 = 0$

Δ=$b^{2} - 4.a.c$

$0^{2} - 4.1. -24\\0 + 96 \\96$

x'= -b ±√Δ / 2.a

$x_{1} = \frac{0 + 9,8}{2.1} = \frac{9,8}{2} = 4,9\\x_{2} = \frac{0 - 9,8 }{2*1} = \frac{-9,8}{2} = -4,9$