Question

si se cumple que:
.
.​

Answer 1

Respuesta:

$(x + y + z) {}^{2} = xy + xz + yz \\ {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + xz + yz) = xy + xz + yz \\ {x}^{2} + {y}^{2} + {z}^{2} = - 1(xy + xz + yz) \\ {x}^{2} + {y}^{2} = - 1(xy + xz + yz) - {z}^{2}$

$M = \frac{x(x + y) + y(y + z)}{z(z + x)} \\ M = \frac{ {x}^{2} + xy + {y}^{2} + yz }{ {z}^{2} + xz} \\ M = \frac{ - 1(xy + xz + yz) - {z}^{2} + xy + yz }{ {z}^{2} + xz } \\ M = \frac{ - xy - xz - yz - {z}^{2} + xy + yz }{ {z}^{2} + xz} \\ M = \frac{ { - z}^{2} - xz }{ {z}^{2} + xz } \\ M = \frac{ - 1( {z}^{2} + xz)}{ 1({z}^{2} + xz)} \\ M = - 1$