Question

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

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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 ) = \dfrac{142}{2}

2

142

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

Hope this helps you bhai...