Question

if x=2+root3 and y=2-root 3 find 1/x3+1/y3​

Answer 1

Answer:

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 )] / [(22 )−( 3 ) 2 ]

=[(2+ 3 )]/[4−3]

=2+ 3

Now,

x−1/x=2− 3

−2− 3

=−23

Let us cube on both sides, we get

(x−1/x) 3

=(−2 3 ) 3x 3 −1/x 3

−3(x)(1/x)(x−1/x)=24 3x 3 −1/x 3 −3(−2/ 3)=−24

3x 3 −1/x 3 +6 3

=−24

3x 3 −1/x 3+6 3 =−24

3x 3 −1/x 3

=−24

3 −6 =3

=−30

Hence,

x 3 −1/x 3

=−303

Step-by-step explanation:

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