Question

If x + 1/x = 5, find the value of x3 + 1/x3

Answer 1

TO FIND:

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

FORMULA USED:

1. ( A )^3 + ( B )^3 = ( A + B ) × ( A^2 + B^2 +AB)
2. ( A + B )^2 = A^2 +B^2 +2AB

SOLUTION:

( x )^3 + 1 / ( x )^3 = ( x+ 1 / x ) × ( x^2 + 1 / x^2 + ( x )( 1 / x ))

( x )^3 + 1 / ( x )^3 = 5 × ( x^2 + 1 / x^2 + 1 ) let this be equation 1

And from 2nd formula

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

5^2 = x^2 + 1 / x^2 + 2

25 = x^2 + 1 / x^2 + 2

x^2 + 1 / x^2 = 25 - 2 =23

x^2 + 1 / x^2 = 23 let this be equation 2

Substitute equation 2 in equation 1

We get,

( x )^3 + 1 / ( x )^3 = 5 × ( x^2 + 1 / x^2 + 1 )

( x )^3 + 1 / ( x )^3 = 5 × ( 23 + 1 )

( x )^3 + 1 / ( x )^3 = 5 × ( 24 )

( x )^3 + 1 / ( x )^3 = 120

ANSWER:

( x )^3 + 1 / ( x )^3 = 120

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