Question

x² + 1/x² = 7 , find the value of x³ + 1/x³

Answer 1

x² + 1/ x² = 7  - (i)

Now add 2 both the sides in (i).

(x+1/x)² = 9

(x + 1/ x) = 3  (ii)

We know that a³ + b³ = ( a+b) ( a²+b²-ab)

So, x³ + 1/x³ = ( x + 1/x) (x² + 1/x² -1)
                     = 3 × (7-1)
                    = 18 

Hope my answer is helpful to u.

Answer 2

Hi ,

x² + 1/x² = 7

x² + 1/x² + 2 = 7 + 2

x² + 1/x² + 2 × x × 1/x = 9

( x + 1/x )² = 3²

x + 1/x = ± 3 ---( 1 )

Now ,

If x + 1/x = 3,

x³ + 1/x³ = ( x + 1/x )³ - 3( x + 1/x )

= 3³ - 3 × 3

= 27 - 9

= 18

If x + 1/x = -3 ,

x³ + 1/x³ = ( - 3 )³ - 3 × ( -3 )

= -27 + 9

= - 18

I hope this helps you.

: )