Correct Answer - Option 2 : 3
Given
x + y + z = 9
x2 + y2 + z2 = 27
(x + y + z)3 = 729
Formula used
(x + y + z)3 = (x + y + z){x2 + y2 + z2 + 2xy + 2yz + 2zx}
Calculation
This is formula (x + y + z)3 = (x + y + z){x2 + y2 + z2 + 2xy + 2yz + 2zx}
⇒ 729 = 9({27 + 2(xy + yz + zx)}
⇒ 81 = 27 + 2(xy + yz + zx)
⇒ 54 = 2(xy + yz + zx)
⇒ (xy + yz + zx) = 27
(xy + yz + zx)/(x + y + z) = 27/9 = 3
∴ The required value of (xy + yx + zx)/(x + y + z) is 3.