Question

If X=3 then find then value of (x1/3 + x—1/3) (x2/3 + x—2/3)

Answer 1

Answer:

18.134

Step-by-step explanation:

$( {x}^{ \frac{1}{3}} + x - \frac{1}{3} )( {x}^{ \frac{2}{3} } + x - \frac{2}{3} ) \\ \\ = {x}^{2} + x + \frac{2}{9} + {x}^{ \frac{5}{3} } + {x}^{ \frac{4}{3} } - x - \frac{2}{3} {x}^{ \frac{1}{3} } - \frac{1}{3} {x}^{ \frac{2}{3} } \\ \\ = {x}^{2} + {x}^{ \frac{5}{3} } + {x}^{ \frac{4}{3} } - \frac{1}{3} {x}^{ \frac{2}{3} } - \frac{2}{3} {x}^{ \frac{1}{3} } + \frac{2}{9} \\ \\ = 18.134$

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Answer 2

Answer:

18.134

Step-by-step explanation:

$\begin{lgathered}( {x}^{ \frac{1}{3}} + x - \frac{1}{3} )( {x}^{ \frac{2}{3} } + x - \frac{2}{3} ) \\ \\ = {x}^{2} + x + \frac{2}{9} + {x}^{ \frac{5}{3} } + {x}^{ \frac{4}{3} } - x - \frac{2}{3} {x}^{ \frac{1}{3} } - \frac{1}{3} {x}^{ \frac{2}{3} } \\ \\ = {x}^{2} + {x}^{ \frac{5}{3} } + {x}^{ \frac{4}{3} } - \frac{1}{3} {x}^{ \frac{2}{3} } - \frac{2}{3} {x}^{ \frac{1}{3} } + \frac{2}{9} \\ \\ = 18.134 \\ \\\end{lgathered}$

(x

3

1

+x−

3

1

)(x

3

2

+x−

3

2

)

=x

2

+x+

9

2

+x

3

5

+x

3

4

−x−

3

2

x

3

1

−

3

1

x

3

2

=x

2

+x

3

5

+x

3

4

−

3

1

x

3

2

−

3

2

x

3

1

+

9

2

=18.134