The roots of the equation x^{2/3} + x^{1/3} - | vedclass

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Question

(C) Given equation: $x^{2/3} + x^{1/3} - 2 = 0$Let $a = x^{1/3}$. Then the equation becomes a quadratic equation in terms of $a$:$a^2 + a - 2 = 0$Fact

Vedclass · Accepted Answer

$1, -8$

Vedclass · Answer

(C) Given equation: $x^{2/3} + x^{1/3} - 2 = 0$Let $a = x^{1/3}$. Then the equation becomes a quadratic equation in terms of $a$:$a^2 + a - 2 = 0$Factorizing the quadratic equation:$a^2 + 2a - a - 2 = 0$$a(a + 2) - 1(a + 2) = 0$$(a - 1)(a + 2) = 0$So,$a = 1$ or $a = -2$.Now,substitute back $a = x^{1/3}$:Case $1$: $x^{1/3} = 1 \implies x = 1^3 = 1$Case $2$: $x^{1/3} = -2 \implies x = (-2)^3 = -8$Thus,the roots are $1, -8$.

The roots of the equation $x^{2/3} + x^{1/3} - 2 = 0$ are

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