Question

pls solve the above mentioned question

Answer 1

let us consider the three varibles m, n and p such that,
${m}^{3} = 8a \\ {n}^{3} = - 64b \\ {p}^{3} = - c$
thus,
$m = 2 \sqrt[3]{a} \\ n = - 4 \sqrt[3]{b} \\ p = - \sqrt[3]{c}$
Now, please consider from a well known formula, if
$a + b + c = 0$
then,
${a}^{3} + {b}^{3} + {c}^{3} = 3abc$
Now, if plugin the values of m, n and p in the above equation, you will see that it satisfies the above mentioned condition.
Thus,
$m + n + p = 0$
or,
$2 \sqrt[3]{a} - 4 \sqrt[3]{b} - \sqrt[3]{c} = 0$
which is correct
thus option a is correct