Question

arata ca : x,(y)+y,(z)+z,(x)=x,y(z)+y,z(x)+z,x(y)

Answer 1

$x.(y) + y.(z) + z.(x) = x.y(z) + y.z(x) + z.x(y)$

$\frac{ \overline{xy} - \overline{x}}{9} + \frac{ \overline{yz} - \overline{y}}{9} + \frac{ \overline{zx} - \overline{z}}{9} = \frac{ \overline{xyz} - \overline{xy}}{90} + \frac{ \overline{yzx} - \overline{yz}}{90} + \frac{ \overline{zxy} - \overline{zx}}{90}$

$\frac{ \overline{xy} - \overline{x} + \overline{yz} - \overline{y} + \overline{zx} - \overline{z}}{9} = \frac{ \overline{xyz} - \overline{xy} + \overline{yzx} - \overline{yz} + \overline{zxy} - \overline{zx}}{90}$

$\frac{ \overline{xy} - \overline{y} + \overline{yz} - \overline{z} + \overline{zx} - \overline{x}}{9} = \frac{ \overline{xyz} - \overline{yz} + \overline{yzx} - \overline{zx} + \overline{zxy} - \overline{xy}}{90}$

$\frac{ \overline{x0} + \overline{y0} + \overline{z0}}{9} = \frac{ \overline{x00} + \overline{y00} + \overline{z00}}{90}$

$\frac{10( \overline{x} + \overline{y} + \overline{z})}{9} = \frac{100( \overline{x} + \overline{y} + \overline{z})}{90}$

$\frac{10( \overline{x} + \overline{y} + \overline{z})}{9} = \frac{10( \overline{x} + \overline{y} + \overline{z})}{9} \: \: (A)$