Question

xpower2/3+xpower1/3-2=0​

Answer 1

$\huge \mathscr{\orange {\underline{\pink{\underline {Answer:-}}}}}$

Given equation is x^⅔  + x^⅓ - 2 = 0

Putting x 1/3  = 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   x^1/3  = y

∴   x^1/3  = - 2  or  x^1/3   = 1

⇒ x = (- 2)³  or x = (1)³

⇒ x = - 8 or x = 1

Hence, roots are -8, 1.