Question

The solutions of $x^{2/5}+3x^{1/5}-4=0$ are

• A. 1, 1024
• B. -1, 1024
• C. 1, 1031
• D. -1024, 1
• E. -1,1031

Answer 1

Answer: (D)

We have,
$x^{\frac{2}{5}}+3x^{\frac{1}{5}}-4=0$
Let $x^{\frac{1}{5}}=y$
$y^2+3y-4=0$
$\Rightarrow y^2+4y-y-4=0$
$\Rightarrow y(y+4)-1(y+4)=0$
$\Rightarrow (y+4)(y-1)=0$
$\Rightarrow y=-4,1$
$\therefore x^{\frac{1}{5}}=-4$ or $x^{\frac{1}{5}}=1$
$\Rightarrow x=(-4{)}^5$ or $x=1$
$\Rightarrow x=-1024$ or $x=1$