Question

Resolva a equação (2x-3) x (2x+1) = (x-2) x 3x

Answer 1

Resposta:

(x=-3,x=1,x=0)

Explicação passo-a-passo:

Answer 2

Explicação passo-a-passo:

$(2x-3) . (2x+1) = (x-2) . 3x\\\\2x.2x+2x.1-3.2x-3.1=x.3x-2.3x\\\\4x^{2} +2x-6x-3=3x^{2} -6x\\\\4x^{2} -4x-3=3x^{2} -6x\\\\4x^{2} -4x-3-3x^{2} +6x=0\\\\x^{2} +2x-3=0$

Resolvendo essa equação por Bhaskara:

Δ=b²-4ac ------> Δ=2²-4.1.(-3) ------->Δ=4+12 ------->Δ=16

Δ(delta)

Encontrando as raízes:

$x_{1} =\frac{-b+\sqrt{delta} }{2a} \\\\x_{2} =\frac{-b-\sqrt{delta} }{2a}$

$x_{1} =\frac{-2+\sqrt{16} }{2.1}\\\\x_{1} =\frac{-2+4}{2} \\\\x_{1} =\frac{2}{2} \\\\x_{1} =1$

$x_{2} =\frac{-b-\sqrt{delta} }{2a}\\\\x_{2} =\frac{-2-\sqrt{16} }{2.1}\\\\x_{2} =\frac{-2-4 }{2}\\\\x_{2} =\frac{-6} {2}\\\\x_{2} =-3$

Resposta: V{-3;1}