If x½= 8, then (x⅓)²=?

Please answer this question. Its urgent ​

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1. *Answer:–

   • Answer: x = 1, x =-8

   Proof:-

   The given equation:-

   x⅔ + x⅓ – 2 = 0

   can be written as (x⅓)² + x⅓ – 2 = 0 ………………………………………………….(1)

   If y = x⅓ then (x⅓)² = y² and (1) →

   y² + y – 2 = 0

   Or, (y² – 1) + y – 1 = 0

   Factorising the quantity within brackets,

   (y+1) (y-1) + (y-1) = 0

   Or, (y-1) (y+1 + 1) =0 [the common factor y-1 is taken out]

   Or, (y – 1) (y + 2) = 0

   Or, y – 1 = 0, y + 2 = 0

   ⇒ y = 1 , y = -2

   ⇒ x⅓ = 1, x⅓ = -2 (∵ y = x⅓)

   Cubing (x⅓)³ = 1³ , (x⅓)³ = (-2)³

   ⇒ x = 1, x = -8 (Answer)

   Verification:-

   x = 1

   L.H.S. of (1) = (x⅓)² + x⅓ – 2 = (1⅓)² + 1⅓ – 2 = 1²+ 1 – 2 = 1² + 1 – 2 = 1+1 = 0 = R.H.S.

   x = -8

   L.H.S. of (1) = (-8⅓)² + (-8)⅓ – 2 = (-2)² – 2 – 2 = 4 – 2 – 2 = 4 – 4 = 0 = R.H.S.

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