Question

If x+y+z = 4, xy + y2 + zx = 1, find the value of x3+y3+z3-3xyz.​

Answer 1

EXPLANATION.

=> x + y + z = 4

=> xy + yz + zx = 1

To find value of x³ + y³ + z³ - 3xyz.

=> ( x + y + z)² = x² + y² + z² + 2 ( xy + yz + zx)

=> ( x + y + z)² = x² + y² + z² + 2 ( 1)

=> ( 4)² = x² + y² + z² + 2

=> 16 = x² + y² + z² + 2

=> 14 = x² + y² + z²

we know that,

=> x³ + y³ + z³ - 3xyz

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

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

=> ( 4)² [ ( 14 - ( 1 ) ]

=> 16 [ 15 ]

=> 240

Therefore,

value of x³ + y³ + z³ - 3xyz = 240