Question

If x^2+1/×^2=47 then find the value of x^3+1/x^3

Answer 1

Hi ,

x² + 1/x² = 47

x² + 1/x² + 2 = 47 + 2

( x + 1/x )² = 49

( x + 1/x )² = 7²

x + 1/x = 7 ---( 1 )

Now ,

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

= 7³ - 3 × 7

= 7( 7² - 3 )

= 7( 49 - 3 )

= 7 × 46

= 322

I hope this helps you.

: )

Answer 2

x² + 1/x² = 47

Adding 2 [ x × 1/x]

x² + 1/x² + 2(x × 2/x) = 47 + 2(x × 1/x)

(x + 1/x)² = 49

x + 1/x = 7

====================

x³ + 1/x³ =>

(x + 1/x) (x² + 1/x² - 1)

(7)(47 - 1)

7 × 46



322




I hope this will help you

(-: