Question

Si: 81/x = x/y = y/z = z/256 = k
halla :x+y+z

Answer 1

81/x = z/256
x/y = y/z  ----   x= y^2/z
substituyendo x en la primera igualdad:

81/ ( y^2/z) = z/256
z 81 / y^2 = z/256
despejando z
81/ y^2 = 1/256
y^2 = 81 (256) = 20736
y = raizcuadrada(20736)
y = 144

Usando  81/x = x/y , despejamos a  x

x^2 = y (81) 
x^2 = 144 (81) = 11664
x = raizcuadrada (11664)
x = 108

x/y = y/z , despejando z se tiene  z = y^2 / x
z = (144)^2 / 108
z = 192

Comprobacion

81 /x = 81/ 108 = 0.75
x/y = 108 / 144 = 0.75
y/z = 144 / 192 = 0.75
z/256 = 192/ 256 = 0.75