Question

what is the value of x^3 + y^3 + z^3 - 3xyz if x^2 + y^2 + z^2 = 83 and x+y+z = 15
pls answer quickly I am in a hurry and I will mark the brainliest

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Answer 1

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 2

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