Question

IF x+1/x=7 then the value of the x³+1/x³is​

Answer 1

Step-by-step explanation:

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.

Answer 2

Answer:

$x^{3}+\frac{1}{x^{3} } = (x+\frac{1}{x} )^{3} - 3*x*\frac{1}{x} (x+\frac{1}{x} )$

$x^{3}+\frac{1}{x^{3} } = (x+\frac{1}{x} )^{3} - 3(x+\frac{1}{x} )$

Insert Values

$x^{3}+\frac{1}{x^{3} } = 7^{3} - 3 * 7$

$x^{3}+\frac{1}{x^{3} } = 7 (7^{2} -3)$

$x^{3}+\frac{1}{x^{3} } = 7(49-3)$

$x^{3}+\frac{1}{x^{3} } =7*46$

$x^{3}+\frac{1}{x^{3} } = 322$