The average of x, y, z is 6 and x - y = 4 xy = 21 what is the value of z?

Question: The average of x, y, z is 6 and x - y = 4 xy = 21 what is the value of z?

Solution:
Given that,
The average of x, y, and z is 6.
⇒ (x + y + z)/3 = 6
⇒ x + y + z = 18 ...........(1)

x - y = 4
x = y + 4 ..........(2)

And
xy = 21 ......... (3)

From (3),
⇒ (y + 4)y = 21
⇒ y² + 4y - 21 = 0
⇒ y² + 7y - 3y - 21 = 0
⇒ y(y + 7) - 3(y + 7) = 0
⇒ (y + 7)(y - 3) = 0
⇒ y = 3, - 7 [Neglecting the negative value]
∴ y = 3

If y = 3, Then x = y + 4 = 3 + 4 = 7

From (2),
∴ x = y + 4 = 3 + 4 = 7

From (1),
⇒ x + y + z = 18
⇒ z = 18 - (7 + 3) = 18 - 10
∴ z = 8