If a1 - 3-b1 - 3-c1 - 3-0Then choose correct option1- a - b - c -02- a-b-c3-27 a b c3- a-b-c-3 a b c4- a3-b3-c3-0Plz explain completely

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Concept of Inequality

If a1 / 3+b1 ...

Question

If a^1/3+ b^1/3 + c ^1/3=0
Then choose correct option
(1). a+b+c=0
(2). (a+b+c)³=27abc
(3). a+b+c=3abc
(4). a³+b³+c³ =0
Plz explain completely

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⎡ ⎢ ⎣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ⎤ ⎥ ⎦

¯ ¯ ¯ a = (a_{1}, a_{2}, a_{3}); ¯ ¯ b = (b_{1}, b_{2}, b_{3})

¯ ¯ c = (c_{1}, c_{2}, c_{3})

a^{\frac{1}{3}} + b^{\frac{1}{3}} + c^{\frac{1}{3}} = 0

(a + b + c)^{3} = 27 a b c

a_{1} b_{1} c_{1}, a_{2} b_{2} c_{2}

a_{3} b_{3} c_{3}

Δ = ∣ ∣ ∣ ∣ \begin{matrix} c_{1} & a_{1} & b_{1} c_{2} & a_{2} & b_{2} c_{3} & a_{3} & b_{3} \end{matrix} ∣ ∣ ∣ ∣

Δ

> 0

\frac{a^{3}}{b^{3}} + \frac{b^{3}}{c^{3}} + \frac{c^{3}}{a^{3}} \geq 3

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