Q53 / 170 · Manipal (MET) 2021 · Mathematics

If $x^{4 / 3}+x^{-1 / 3}=1, x^5+3 x^2-x$ is equal to

  • A
    0
  • B
    1
  • Correct answer
    C
    -1
  • D
    2

Solution

$\begin{aligned} & x^{4 / 3}+x^{-1 / 3}=1 \Rightarrow x^{4 / 3} \cdot x^{1 / 3}+1=x^{1 / 3} \\ & \Rightarrow \quad x^{5 / 3}-x^{1 / 3}=-1\end{aligned}$ On cubing both sides, we get $\begin{array}{rr} & x^5-x-3 x^2\left(x^{5 / 3}-x^{1 / 3}\right)=-1 \\ \Rightarrow & x^5-x+3 x^2=-1\end{array}$

Hence, the correct answer is option: 'C'.

Relevant Questions