Question

x=a^1/3-a^-1/3 then x^3+3x-a=________________

Answer 1

Answer:

-1/a

Step-by-step explanation:

x=a^1/3-a^-1/3 ---------1

cube on both sides

x³= a^(3*1/3) - a^(3*-1/3) - 3(a^1/3)(a^-1/3)(a^1/3-a^-1/3)

[since (a - b)³ = a³ - b³ -3ab(a - b)]

= a¹ - a^-1 - 3(a^(1/3 -1/3))(a^1/3-a^-1/3)

= a - 1/a - 3(a^0)(x). [ since ------1]

= a - 1/a -3(1)(x)

= a - 1/a -3x

therefore, x³+3x-a = a - 1/a -3x +3x -a

= -1/a