Solveeit Logo
Login

Question

Question: If \(y = - \left( x^{3} + \frac{x^{6}}{2} + \frac{x^{9}}{3} + ........ \right)\), then \(x =\)...

If y=−(x3+x62+x93+........)y = - \left( x^{3} + \frac{x^{6}}{2} + \frac{x^{9}}{3} + ........ \right), then x=x =

A

1+ey3\frac{1 + e^{y}}{3}

B

1−ey3\frac{1 - e^{y}}{3}

C

(1−ey)13(1 - e^{y})^{\frac{1}{3}}

D

(1−ey)3(1 - e^{y})^{3}

Answer

(1−ey)13(1 - e^{y})^{\frac{1}{3}}

Explanation

Solution

y=−[x3+(x3)22+(x3)33+........]=log⁡e(1−x3)y = - \left\lbrack x^{3} + \frac{(x^{3})^{2}}{2} + \frac{(x^{3})^{3}}{3} + ........ \right\rbrack = \log_{e}(1 - x^{3})

⇒ ey=1−x3e^{y} = 1 - x^{3} ⇒ x=(1−ey)13x = (1 - e^{y})^{\frac{1}{3}}