x+1/x=square root 5 then the value of x^3+1/x^3=?
Answers
Answered by
5
★Heya★
x + 1/x = √5
CUBING ON BOTH SIDE'S WE HAVE
( x + 1/x )³ = (√5)³
=>
x³ + 1/x³ + 3 ( x + 1/x ) = √5 × √5 × √5
Becoz
( a + b )³ = a³ + b³ + 3ab ( a + b )
=>
x³ + 1/x³ + 3√5 = 5√5
=>
x³ + 1/x³ = 5√5 - 3√5
=>
x³ + 1/x³ = √5 ( 5 - 3 )
=>
x³ + 1/x³ = 2√5
x + 1/x = √5
CUBING ON BOTH SIDE'S WE HAVE
( x + 1/x )³ = (√5)³
=>
x³ + 1/x³ + 3 ( x + 1/x ) = √5 × √5 × √5
Becoz
( a + b )³ = a³ + b³ + 3ab ( a + b )
=>
x³ + 1/x³ + 3√5 = 5√5
=>
x³ + 1/x³ = 5√5 - 3√5
=>
x³ + 1/x³ = √5 ( 5 - 3 )
=>
x³ + 1/x³ = 2√5
Similar questions