Question

if x=2+√3 find the value of x³+1/x³

Answer 1

Hi ,

x = 2 + √3 -----( 1 )

1/x = 1/ ( 2 + √3 )

= ( 2 - √3 ) / [ ( 2 + √3 ) ( 2 - √3 )]

= ( 2 - √3 ) / ( 4 - 3 )

= 2 - √3 ------( 2 )

x + 1/x = 2 + √3 + 2 - √3

x + 1/ x = 4 ------( 3 )


We know that

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

= 4³ - 3 × 4

= 64 - 12

= 52

I hope this helps you.

:)