If x1 / 3 + y1 / 3 = z1 / 3 , then {(x + y

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If x^{1 / 3} + y^{1 / 3} = z^{1 / 3} , then {(x + y – z)³ + 27xyz} equals :

1. –1
2. 1
3. 0
4. 27

Correct Option: C

Using Rule 8,
x^{1 / 3} + y^{1 / 3} = z^{1 / 3} ......(i)
Cubing both sides,
( x^{1 / 3} + y^{1 / 3} = z^{1 / 3} )³ = z
⇒ x + y + 3 x^{1 / 3} . y^{1 / 3} ( ^{1 / 3} + y^{1 / 3} ) = z
[∴ (a + b)³ = a³ + b³ + 3ab (a + b)]
⇒ x + y – z = - 3 x^{1 / 3} . y^{1 / 3} .z^{1 / 3} ......(ii) [From equation (i)]
∴ (x + y – z)³ + 27xyz = [ - 3x^{1 / 3} . y^{1 / 3} . z^{1 / 3} ]³ + 27xyz [From equation (ii)]
= – 27xyz + 27xyz = 0