Question

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

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

32

Step-by-step explanation:

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 )

x³ + y³ + z³ - 3xyz

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

= 8 × [ 24 - 20]

= 8 × 4

= 32