Question

a2-3a+1=0 then find a3+1/a3

Answer 1

Solution :

Given a² - 3a + 1 = 0

=> a² + 1 = 3a

divide each term by a , we get

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

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We know the algebraic identity :

x³ + y³ + 3xy( x + y ) = ( x + y )³

Or

x³ + y³ = ( x + y )³ - 3xy( x + y )

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Now ,

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

= 3³ - 3 × 3 [ from ( 1 ) ]

= 27 - 9

= 18

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Answer 2

this is the answer of this question