in Quantitative Aptitude recategorized by
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The roots of the equation $x^{2/3}+x^{1/3}-2=0$ are :

  1. $1, -8$
  2. $-1, -2$
  3. $\frac{2}{3}, \frac{1}{3}$
  4. $-2, -7$
in Quantitative Aptitude recategorized by
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(A) $1, -8$

$x^{\frac{2}{3}} + x^{\frac{1}{3}} – 2 = 0\\  \> \\  \text{put }x=1 \\  \implies 1 + 1-2 = 0 \\ \> \\ \text{put } x= -8 \\ \implies (-8)^{\frac{2}{3}} + (-8)^{\frac{1}{3}} – 2 = 4-2 -2 = 0$
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Another method, putting $x^{\frac{1}{3}} = y$, so equation will become $y^{2} +y-2 =0$

On solving, we will get values as y = -2 , 1 

So, x = $y^{3}$ = $-2^{3}$, $1^{3}$ = -8, 1

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