If x + y + z = 8 and xy + yz + zx = 20, find the value of x^3 + y^3 + z^3- 3xyz
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4
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Step-by-step explanation:
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11
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32
Step-by-step explanation:
x + y + z = 8 -----( 1 )
xy + yx + zx = 20 ----( 2 )
do the square of equation ( 1 ),
( x + y + z )² = 8²
x² + y² + z² + 2 ( xy + yz + zx ) = 64
x² + y² + z² + 2 × 20 = 64
x² + y² + z² = 64 - 40
x² + y² + z² = 24 ----( 3 )
x³ + y³ + z³ - 3xyz
= ( x + y + z ) [ x² + y² + z² - ( xy + yz + zx ) ]
= 8 × [ 24 - 20]
= 8 × 4
= 32
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