Question

find the value of x^3 +y^3+z^3-3xyz.if x+y+z=15 and x^2+y^2+z^2= 51​

Answer 1

Answer:

-540

Step-by-step explanation:

Given---> x+ y + z = 15 , x² + y²+ z² = 51

To find ---> Value of x³ + y³ + z³ - 3xyz

Solution---> ATQ , x + y + z = 15 , x² + y² + z² = 51

Now, x + y + z = 15

Squaring both sides we get

( x + y + z )² = ( 15 )²

=> x² + y² + z² + 2xy + 2yz + 2zx = 225

=>( x² + y² + z² ) + 2 (xy + yz + zx ) = 225

=> ( 51 ) + 2 (xy + yz + zx ) = 225

=> 2 ( xy + yz + zx ) = 225 - 51

=> 2 ( xy + yz + zx ) = 174

=> xy + yz + zx = 174 / 2

=> xy + yz + zx = 87

Now we find value of

x² + y² + z² - xy - yz - zx = (x² +y² +z²) - (xy+yz+zx)

= ( 51 ) - ( 87 )

= - 36

Now , x³ + y³ + z³ - 3xyz

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

= ( 15 ) ( - 36 )

= - 540