Question

x+y+z+xy+yz+zx+xyz=384 Find x+y+z???​

Answer 1

Answer:

x + y + z = 20

Step-by-step explanation:

x y z + xy + y z + x z + x + y + z = 384

x y ( z + 1) + z ( x + y) + (x + y) + z = 384

x y (z + 1) + ( x + y ) ( z + 1) + z = 384

add 1 to both the sides

x y (z + 1) + (x + y)(z + 1) +( z + 1) = 384 +1

(z + 1) ( xy + x+y + 1) = 385

( z + 1) {x(y+1) + 1( y+1)} = 385

( z + 1) ( y + 1) ( x + 1) = 5 x 7 x 11

(x+1), (y+1), (z+1) hold either of these values. 5 or 7 or 11

x, y, z hold either of the values 4, 6 , or 10

Hence, x + y + z = 4 + 6 + 10 = 20