Question

Find the value of x3 + y3 + z3 – 3xyz if x2 + y2 + z2 = 83 and x + y + z = 15

Answer 1

Answer:

Given :

x² + y² + z² = 83

And

x + y + z = 15

To Find :

The value of ,  x³ + y³ + z³ - 3 x y z

Solution :

∵  ( x + y + z )² = x² + y² + z² + 2 ( x y + y z + z x )

And

x + y + z = 15

So,  83 + 2 ( x y + y z + z x ) = ( 15 )²

Or, 2 ( x y + y z + z x ) = 225 - 83

Or, 2 ( x y + y z + z x ) = 142

∴ ( x y + y z + z x ) =

i.e   ( x y + y z + z x ) = 71

Again

∵  x³ + y³ + z³ - 3 x y z = ( x + y + z ) [ ( x² + y² + z² ) - ( x y + y z + z x ) ]

Or,                                = ( 15 ) × [ 83 - 71 ]

Or,                                = 15 × 12

i.e                                 = 180

Hence, The value of  x³ + y³ + z³ - 3 x y z is 180 . Answer

Step-by-step explanation:

Answer 2

Step-by-step explanation:

I am not sure but let us give a try.

Take out the 3 in common.

3(x+y+z-xyz).

Now the value of x+y+z= 15 is given so put the value.

3(15-xyz)= (3×15)-(3×xyz)

=75-3xyz