Question

If x^1/3 + y^1/3 + z^1/3 = 0, then what is (x + y + z)³ equal to ?

(a) 1 

(b) 3 

(c) 3xy 

(d) 27xyz

Answer 1

(d) 27 xyz.

If x^1/3 + y^1/3 + z^1/3 = 0, then 

(x^1/3)³ + (y^1/3)³ + (z^1/3)³ = 3x^1/3y^1/3z^1/3

⇒ x + y + z = 3x^1/3 y^1/3 z^1/3 

Now taking the cube of both the sides, we have 

(x + y + z)³ = (3x^1/3 y^1/3 z^1/3)³ = 27 xyz.