Question

If x^2+1/x^2=7,find the value of x^3+1/x^3

Answer 1

This is the answer.If not clear, please reply.

Answer 2

Given

x^2 + 1/x^2 = 7

To Find

x^3 + 1/x^3

Solution

( x + 1/x )^2 = ( x )^2 + ( 1/x )^2 + 2 ( x ) ( 1/x )

( x + 1/x )^2 = x^2 + 1/x^2 + 2

( x + 1/x )^2 = 7 + 2

( x + 1/x )^2 = 9

( x + 1/x ) = 3

or. ( x + 1/x ) = - 3

if ( x + 1/x ) = 3

than

( x + 1/x )^3 = ( x )^3 + ( 1/x )^3 + 3 (x )( 1/x ) ( X + 1/x )

( 3 )^3 = x^3 + 1/x^3 + 3 ( 3 )

27 = x^3 + 1/x^3 + 9

x^3 + 1/x^3 = 18

if x + 1/x = - 3

than

( x + 1/x )^3 = x^3 + 1/x^3 + 3 ( x + 1/x )

( - 3 )^3 = x^3 + 1/x^3 + 3 ( - 3 )

- 27 = x^3 + 1/x^3 - 9

x^3 + 1/x^3 = - 18