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What values of $x$ satisfy $x^{\frac{2}{3}} + x^{\frac{1}{3}} - 2 \leq 0?$

  1. $-8 \leq x \leq 1$
  2. $-1 \leq x \leq 8$
  3. $1 < x < 8$
  4. $1 \leq x \leq 8$
  5. $-8 \leq x \leq 8$
in Quantitative Aptitude edited by
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Method 1:$x^{\frac{2}{3}} + x^{\frac{1}{3}} -2$ ≤ 0

put x=8

$8^{\frac{2}{3}} + 8^{\frac{1}{3}} -2 =4$

and 4 ≰ 0

Hence,we can eliminate option (2),(4) and (5)

now put x=7

$7^{\frac{2}{3}} + 7^{\frac{1}{3}} -2$ ≰ 0

From here we can eliminate option (3) too.

 

Method 2: $x^{\frac{2}{3}} + x^{\frac{1}{3}} -2$ ≤ 0

we can rewrite this equation as

$(x^{\frac{1}{3}}-1) (x^{\frac{1}{3}}+2)$

-8 ≤ x ≤ 1

 

Hence,Option(1) -8 ≤ x ≤ 1 is the correct choice.

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