Question

if (x-1/x)=7,then find the value of x^3-1/x^3. ​

Answer 1

Answer:

It is given that x+

x

1

=7, by taking cubes on both sides we get:

(x+

x

1

)

3

=7

3

⇒(x)

3

+(

x

1

)

3

+(3×x×

x

1

)(x+

x

1

)=343(∵(a+b)

3

=a

3

+b

3

+3ab(a+b))

⇒x

3

+

x

3

1

+3(7)=343(Givenx+

x

1

=7)

⇒x

3

+

x

3

1

+(3×7)=343

⇒x

3

+

x

3

1

+21=343

⇒x

3

+

x

3

1

=343−21

⇒x

3

+

x

3

1

=322

Hence, x

3

+

x

3

1

=322.

Step-by-step explanation:

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