Question

If y = x^1/3-x^-1/3 then y^(3+3y) is​

Answer 1

Given : y = x^1/3 - x^-1/3

To Find :  y³ + 3y

Solution:

y = x^1/3 - x^-1/3

=> y = x^1/3 - 1/x^1/3

Taking cube both sides

=> y³ = (x^1/3 - 1/x^1/3)³

using identity

(a - b)³  = a³  - b³  - 3ab(a - b)

=> y³ =  (x^1/3)³ - (1/x^1/3)³ - 3(x^1/3)(1/x^1/3)(x^1/3 - 1/x^1/3)

=>  y³ =  x - 1/x - 3(x^1/3 - 1/x^1/3)

y = x^1/3 - 1/x^1/3

=> y³ =  x - 1/x - 3y

=>  y³ + 3y = x - 1/x

y³ + 3y = x - 1/x

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