Question

The real root of the equation $x^3+12x-12=0$, is:

• A. $2\sqrt[3]{32}-\sqrt[3]{35}$
• B. $2\sqrt[3]{32}+\sqrt[3]{35}$
• C. $2\sqrt[3]{32}+\sqrt[3]{34}$
• D. $2\sqrt[3]{32}-\sqrt[3]{34}$

Answer 1

Answer: (D)

$2\sqrt[3]{32}-\sqrt[3]{34}$

We know $z^3+3hz+g=0$ have a real root $z=\sqrt[3]{3p}+\sqrt[3]{3q}$
when $\sqrt[3]{3pq}=-h$
Using this for
$x^3+12x-12=0$
From options
A) $2\sqrt[3]{32}-\sqrt[3]{35}\sqrt[3]{316}\sqrt[3]{3-5}\ne -4$
B) $2\sqrt[3]{32}+\sqrt[3]{35}\sqrt[3]{316}\sqrt[3]{35}\ne -4$
C) $2\sqrt[3]{32}+\sqrt[3]{34}\sqrt[3]{316}\sqrt[3]{34}=4\ne -4$
D) $2\sqrt[3]{32}-\sqrt[3]{34}\sqrt[3]{3-16}\sqrt[3]{34}=-4$
Hence, option D is correct answer