Question

if x^2+(1/x)=2=x+(1/x^2) then the value of x^3+(1/x^2) for x>0 is​

Answer 1

Answer:

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

)]/[(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