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Question
Solve x2/3 + x1/3 - 2 = 0.
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Solution
Given equation is x2/3 + x1/3 - 2 = 0
Putting x1/3 = y, the given equation becomes
y2 + y - 2 = 0
⇒ y2 + 2y - y - 2 = 0
⇒ y(y + 2) - 1(y + 2) = 0
⇒ (y + 2) (y - 1) = 0
⇒ y + 2 = 0 or y - 1 = 0
⇒ y = -2 or y = 1
But x1/3 = y
∴ x1/3 = -2 or x1/3 = 1
⇒ x =(-2)3 or x = (1)3
⇒ x = -8 or x = 1
Hence, roots are -8, 1.
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