Question

5. If (a+1/a)^2=3, then the value of (a^3+1/a^3) is

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Answer 1

GOOD MORNING!

( x³ + y³ ) = ( x + y )³ - 3xy ( x + y )

( a³ + 1/a³ ) = ( a + 1/a )³ - 3( a + 1/a )

{ ( a + 1/a )² = 3 ... ( Given ) }

( a + 1/a ) = ±√3

( a³ + 1/a³ ) = ( ±√3 )³ - 3 ( ±√3 )

( a³ + 1/a³ ) = 3√3 + 3√3

OR

( a³ + 1/a³ ) = -3√3 + 3√3

( a³ + 1/a³ ) = 6√3

OR

( a³ + 1/a³ ) = 0