Question

pleas answer this by using identiy

Answer 1

Hi ,

x - 1/x = 3 + 2√2 -----( 1 )

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We know the algebraic identity ,

a³ - b³ - 3ab( a - b ) = ( a - b )³

Or

a³ - b³ = ( a - b )³ + 3ab( a - b )

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x³ - 1/x³ = ( x - 1/x )³ + 3×x × 1/x(x - 1/x )

= ( x - 1/x )³ + 3( x - 1/x )

= ( 3 + 2√2 )³ + 3( 3 + 2√2 )

= ( 3 + 2√2 ) [ (3 + 2√2 )² + 3 ]

= ( 3 + 2√2 ) [ 9 + 8 + 12√2 + 3 ]

= ( 3 + 2√2 ) [ 20 + 12√2 ]

= 60 + 36√2+ 40√2 + 48

= 108 + 76√2

I hope this helps you.

: )