Find the value of x4+y^^4

Question

If x3 + y3 = 9 and x + y = 3, then the value of x4+y4 is,

Answer 1

Given x3 + y3 = 9 and x + y = 3            

(x + y)^3  =   x3 + y3  + 3xy(x + y)

Substitute x3 + y3 = 9 and x + y = 3  in above equation

(3)^3  =   9 + 3xy(3)

27  =   9 + 9xy

27 - 9  =   9xy

9xy  =  18

xy  =  18/9

xy  =  2  

x3 + y3  =  (x + y)( x^2  - xy + y^2  )

Substitute x3 + y3 = 9, x + y = 3 and xy = 2 in above equation

9  =  (3)( x^2  - 2 + y^2)

9/3  =  ( x^2  - 2 + y^2)

3  =  ( x^2  - 2 + y^2)

x^2 + y^2  =  3 + 2

x^2 + y^2  =  5

Apply Square on each side

(x^2 + y^2)^2  =  5^2

 x4 + y4  + 2(x^2)(y^2)  =  25

 x4 + y4  + 2(xy)^2  =  25

 x4 + y4  + 2(2)^2  =  25                              [ Since xy = 2 ]

 x4 + y4  + 2(4)  =  25

 x4 + y4  + 8  =  25

 x4 + y4  =  25 - 8

 x4 + y4  =  17

Answer :

The Value of  x4 + y4  is  17.