Question

If $ {{x}^{2/3}}-7{{x}^{1/3}}+10=0 $ then, the value of $ x $ is

• A. $ \{125\} $
• B. $ \{8\} $
• C. $ \phi $
• D. $ \text{ }\!\!\{\!\!\text{ 125,8 }\!\!\}\!\!\text{ } $

Answer 1

Answer: (D)

Given equation can be rewritten as
$\left(x^{1 / 3}\right)^{2}-7\left(x^{1 / 3}\right)+10=0$
Let $\alpha=x^{1 / 3}$ then I t reduces to
$\alpha^{2}-7 \alpha+10=0$
$\Rightarrow (\alpha-5)(\alpha-2)=0$
$\Rightarrow \alpha=5,2$
$\therefore \alpha^{3}=x$
$\Rightarrow x=125$ and $8$
$ \cos e c^{-1}(\sec \alpha)+\cot ^{-1}(\tan \alpha)$