Question

x+1/x = a then find the value of x^3+x^2+1/x^3+1/x^2

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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

)]/[(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

Step-by-step explanation:

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Answer 2

Answer:

Given, x−

x

1

=5

Squaring both the sides,

⇒(x−

x

1

)

2

=5

2

⇒x

2

+

x

2

1

−2(x)(

x

1

)=25

⇒x

2

+

x

2

1

=25+2

⇒x

2

+

x

2

1

=27

Now,

x

3

−

x

3

1

=(x−

x

1

)[(x)

2

+(

x

1

)

2

+(x)(

x

1

)]

=5(27+1)

=140