Find the value of x3+y3+z3=83 and x+y+z=15

x² + y² + z² = 83

AND

x + y + z = 15

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:

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

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