Question

(x-1) x (x-2) = (x-1) x (2x+3)

Answer 1

Resposta:

x'=-1-√2

x"= -1+√2

∆= 2√2

Explicação passo-a-passo:

$(x + 1)(x - 2) = (x - 1)(2x + 3) \\ {x}^{2} - 2x + x - 2 = 2 {x}^{2} + 3x - 2x - 3 \\ {x}^{2} - 2x + x - 2 {x}^{2} - 3x + 2x = - 1 \\ - {x}^{2} - 2x = - 1 \\ {x}^{2} + 2x - 1 = 0 \\a = 1 \\ b = 2 \\ c = - 1 \\ ∆ = 4 + 4 = 8 \\ \sqrt{∆} = 2 \sqrt{2} \\ x _{1} = \frac{ - 2 + 2 \sqrt{2} }{2} = \frac{2( - 1 \sqrt{2} )}{2} = - 1 + \sqrt{2} \\ x _{2} = \frac{ - 2 - 2\sqrt{2} }{2} = \frac{ 2( - 1 - \sqrt{2} )}{2} = - 1 - \sqrt{2}$