Diketahui 3x, 4y, dan 5z adalah tiga suku membentuk barisan geometri dan 1/x 1/y dan 1/z membentuk barisan aritmatika. maka, z/x + x/z = ... A. 7/15 B. 14/15 C.

Geometri : 3x, 4y, 5z
=> 4y/3x = 5z/4y
=> 15xz = 16y^2
=> xz = (16y^2)/15

Aritmatika : 1/x, 1/y, 1/z
1/y - 1/x = 1/z - 1/y
1/y + 1/y = 1/x + 1/z
2/y = (z + x)/xz
y(z + x) = 2xz
y(z + x) = 2(16y^2)/15
(z + x) = (32y^2)/15y
(z + x) = (32y)/15
(z + x)^2 = ((32y)/15)^2
z^2 + 2xz + x^2 = (1024y^2)/225
z^2 + 2(16y^2/15) + x^2 = (1024y^2)/225
z^2 + x^2 = (1024y^2)/225 - (32y^2)/15
z^2 + x^2 = (1024y^2 - 480y^2)/225
z^2 + x^2 = (544y^2)/225

z/x + x/z = (z^2 + x^2)/(xz)
= ((544y^2)/225) / (16y^2/15)
= 544y^2/225 . 15/(16y^2)
= 34/15