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 = x³ + y³ + z³ - 3xyz

SOLUTION

( x + y + z )² = x² + y² + z² + 2 ( xy + yz + zx )

AND x + y + z = 15

SO, 83 + 2 ( xy + yz + zx ) = (15)²

83 + 2 ( xy + yz + zx ) = 225

2 ( xy + yz + zx ) = 225 - 83

2 ( xy + yz + zx ) = 142

( xy + yz + zx ) = 142/2

( xy + yz + zx ) = 71

AGAIN

x³ + y³ + z³ - 3xyz = ( x + y + z ) [ ( x²+ y² + z² ) - ( xy + yz + zx ) ]

OR, = 15 × [ 83 - 71 ]

= 15 × 12

= 180

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Answer 2

Answer:

180

Step-by-step explanation:

GIVEN = x² + y² + z² = 83

AND

x + y + z = 15

TO FIND = x³ + y³ + z³ - 3xyz

SOLUTION

( x + y + z )² = x² + y² + z² + 2 ( xy + yz + zx )

AND x + y + z = 15

SO, 83 + 2 ( xy + yz + zx ) = (15)²

83 + 2 ( xy + yz + zx ) = 225

2 ( xy + yz + zx ) = 225 - 83

2 ( xy + yz + zx ) = 142

( xy + yz + zx ) = 142/2

( xy + yz + zx ) = 71

AGAIN

x³ + y³ + z³ - 3xyz = ( x + y + z ) [ ( x²+ y² + z² ) - ( xy + yz + zx ) ]

OR, = 15 × [ 83 - 71 ]

= 15 × 12

= 180