If a^ 1 3 +b^ 1 3 +c^ 1 3 =0, than.

MCQ

If $\text{a}^{\frac{1}{3}}+\text{b}^{\frac{1}{3}}+\text{c}^{\frac{1}{3}}=0,$ than.

A
$a^3+b^3+c^3=0$
B
$a + b + c$
✓
$(a+b+c)^3=27 a b c$
D
$a + b + c = 3abc$

✓

Answer

Correct option: C.

$(a+b+c)^3=27 a b c$

$\text{a}^{\frac{1}{3}}+\text{b}^{\frac{1}{3}}+\text{c}^{\frac{1}{3}}=0$
$\Rightarrow\text{a}^{\frac{1}{3}}+\text{b}^{\frac{1}{3}}=-\text{c}^{\frac{1}{3}}$
$\Rightarrow\Big[(\text{a}^{\frac{1}{3}})(\text{b}^{\frac{1}{3}})\Big]^3=\Big(-\text{c}^{\frac{1}{3}}\Big)^3$
$\Rightarrow\text{a}+\text{b}+\Big[3\times\text{a}^{\frac{1}{3}}\times\text{b}^{\frac{1}{3}}\Big(\text{a}^{\frac{1}{3}}+\text{b}^{\frac{1}{3}}\Big)\Big]=-\text{c}$
$\Rightarrow\text{a}+\text{b}+3\times\text{a}^{\frac{1}{3}}\times\text{b}^{\frac{1}{3}}\Big(-\text{c}^{\frac{1}{3}}\Big)=-\text{c}$
$\Rightarrow\text{a}+\text{b}+\text{c}=3\times\text{a}^{\frac{1}{3}}\times\text{b}^{\frac{1}{3}}\times\text{c}^{\frac{1}{3}}$
$\Rightarrow(\text{a}+\text{b}+\text{c})^3=\Big(3\times\text{a}^{\frac{1}{3}}\times\text{b}^{\frac{1}{3}}\times\text{c}^{\frac{1}{3}}\Big)$
$\Rightarrow(\text{a}+\text{b}+\text{c})^3=27\text{abc}$