If x=
[tex] \sq 3 \sqrt{2 + \sqrt{3} } [/tex]
,then x³+1/x³ is​

1 thought on “If x= <br />[tex] \sq 3 \sqrt{2 + \sqrt{3} } [/tex]<br /> ,then x³+1/x³ is​”

1. Step-by-step explanation:

   It is given that,

   x=2−

   3

   so,

   1/x=1/(2−

   3

   )

   By rationalizing the denominator, we get

   =[1(2+

   3

   )]/[(2−

   3

   )(2+

   3

   )]

   =[(2+

   3

   )]/[(2

   2

   )−(

   3

   )

   2

   ]

   =[(2+

   3

   )]/[4−3]

   =2+

   3

   Now,

   x−1/x=2−

   3

   −2−

   3

   =−2

   3

   Let us cube on both sides, we get

   (x−1/x)

   3

   =(−2

   3

   )

   3

   x

   3

   −1/x

   3

   −3(x)(1/x)(x−1/x)=24

   3

   x

   3

   −1/x

   3

   −3(−2/

   3

   )=−24

   3

   x

   3

   −1/x

   3

   +6

   3

   =−24

   3

   x

   3

   −1/x

   3

   +6

   3

   =−24

   3

   x

   3

   −1/x

   3

   =−24

   3

   −6

   3

   =−30

   3

   Hence,

   x

   3

   −1/x

   3

   =−30

   3

   Reply