if x-1/x=√3,find x³-1/x³
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Answer:
x - 1 / x = 3
On cubing both sides ;
( x - 1 / x ) = ( 3 )³
Using Identity :
( a - b )³ = a³ - b³ - 3 ab ( a - b )
⇒ x³ - 1 / x³ - 3 ( x - 1 / x ) = 27
⇒ x³ - 1 / x³ - 3 ( 3 ) = 27
⇒ x³ - 1 / x³ - 9 = 27
⇒ x³ - 1 / x³ = 27 + 9
⇒ x³ - 1 / x³ = 36
Hence, the answer is 36.
Step-by-step explanation:
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