Question

Seja m x, y, z e w soluções do sistema :
x+ y=0
y+ z=0
z+ w=1
y+ w=0
Então, o produto x. y. z. w vale?

Answer 1

$x + y = 0 \\ y + z = 0 \\ z + w = 1 \\ y + w = 0 \\ \\ z + w = 1 \: \: \: \: ( \times - 1) \\ y + w = 0 \\ \\ - z - w = - 1 \: \: \: (soma \: as \: duas) \\ y + w = 0 \\ \\ - z + y = - 1 \\ \\ y + z = 0 \: \: \: \: (soma \: as \: duas) \\ - z + y = - 1 \\ \\ 2y = - 1 \\ y = \frac{ - 1}{2} \\ \\ y + z = 0 \\ \frac{ - 1}{2} + z = 0 \\ z = \frac{1}{2} \\ \\ x + y = 0 \\ x - \frac{1}{2} = 0 \\ x = \frac{1}{2} \\ \\ z + w = 1 \\ \frac{1}{2} + w = 1 \\ w = \frac{1}{2} \\ \\ x \times y \times z \times w = \\ \frac{1}{2} \times \frac{ -1 }{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{ - 1}{16}$

Resposta final : -1/16