Question

If x+y+z=8 and xy+yz+zx=20, find the value if x 3+y 3+x 3 -3xyz

Answer 1

Hi ,

x + y + z = 8 -----( 1 )

xy + yx + zx = 20 ----( 2 )

do the square of equation ( 1 ),

( x + y + z )² = 8²

x² + y² + z² + 2 ( xy + yz + zx ) = 64

x² + y² + z² + 2 × 20 = 64

x² + y² + z² = 64 - 40

x² + y² + z² = 24 ----( 3 )

Now ,..

x³ + y³ + z³ - 3xyz

= ( x + y + z ) [ x² + y² + z² - ( xy + yz + zx ) ]

= 8 × [ 24 - 20]

= 8 × 4

= 32

I hope this helps you.

:)

Answer 2

x + y + z = 8 -----( 1 )  xy + yx + zx = 20 ----( 2 )  do the square of equation ( 1 ),  ( x + y + z )² = 8²  x² + y² + z² + 2 ( xy + yz + zx ) = 64  x² + y² + z² + 2 × 20 = 64  x² + y² + z² = 64 - 40  x² + y² + z² = 24 ----( 3 )  Now ,..  x³ + y³ + z³ - 3xyz   = ( x + y + z ) [ x² + y² + z² - ( xy + yz + zx ) ]  = 8 × [ 24 - 20]  = 8 × 4  = 32