A) \( \Large 3x^{\frac{1}{3}}.y^{\frac{1}{3}}.z^{\frac{1}{3}} \) |
B) \( \Large 9x^{\frac{2}{3}}.y^{\frac{2}{3}}.z^{\frac{2}{3}} \) |
C) \( \Large 27 xyz \) |
D) 0 |
C) \( \Large 27 xyz \) |
Given : \( \Large x^{\frac{1}{3}}+y^{\frac{1}{3}} = -z^{\frac{1}{3}} \)
Cubing, \( \Large \left(x^{\frac{1}{3}}+y^{\frac{1}{3}}\right)^{3} = \left(-z^{\frac{1}{3}}\right)^{3} \)
=> \( \Large x+y+3x^{\frac{1}{3}}y^{\frac{1}{3}} \left(x^{\frac{1}{3}}+y^{\frac{1}{3}}\right) = -z \)
=> \( \Large x+y+3 x^{\frac{1}{3}} y^{\frac{1}{3}} \left(-z^{\frac{1}{3}}\right) = -z \)
=> \( \Large x+y+z = 3 x^{\frac{1}{3}} y^{\frac{1}{3}} z^{\frac{1}{3}} \)
Again cubing, \( \Large \left(x+y+z\right)^{3} = 27 xyz. \)