Question

Ifx^2+1/x^2=27find the value of x^3-1/x^3

Answer 1

Heya!!

x² + 1/x² = 27 { Given }

Find x³ - 1/x³

x² + 1/x² = ( x - 1/x )² + 2

Becoz a² + b² = ( a - b )² + 2ab

( x - 1/x )² = 27 - 2

( x - 1/x )² = 25

( x - 1/x ) = ±√(25)

( x - 1/x ) = ±5

CUBING on both sides we have.

( x - 1/x )³ = (±5)³

x³ - 1/x³ - 3 ( x - 1/x ) = ±125

Becoz {a - b}³ = a³ - b³ -3ab ( a - b )

x³ - 1/x³ = ±125 + ( ±5 )

x³ - 1/x³ = 130

OR

x³ - 1/x³ = -130