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