Question

Știind că x+y+z=9,Calculați xyz barat + yzx barat + zxy barat

Answer 1

xyz+yzx+zxy=

=100x+10y+z+100y+10z+z+100z+10x+y

=111x+111y+111z

=111(z+y+z)

=111·9

=999

Answer 2

$\it x+y+z = 9\ \ \ \ (*)$

[tex]\it \overline{xyz} +\overline{yzx} +\overline{zxy} = 100x+10y+z+100y+10z+x+100z+10x+y \\\;\\ = 111x+111y+111z= 111(x+y+z) \stackrel{(*)}{=} 111\cdot9=999[/tex]