Question

if ( x^2 + 1/x^2) = 7. find the value of ( x^3 + 1/x^3 )​

Answer 1

Answer:

Ifx

2

+1/x

2

−7 find the valve of x

3

+1/3

3

Given equation is x

2

+1/x

2

=7

we know that(x+1/x)

2

=x

2

+2.x.1/x+(1/x)

2

=x

2

+2+1/x

2

=(x

2

+1/x

2

)+2

=7+2

=9.

∴(x+1/x)

2

=9

⇒(x+1/x)=

(3)

x

⇒(x+1/x)=3.

Now ,

(x

3

+1/x)

3

=(x+1/x)

3

−3.x.1/x.(x+1/x)

=(x+1/x)

3

−3(x+1/x)

=(3)

3

−3(3)

=27−9

=18.

∴x

3

+1/x

3

=18.

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