Question

. If x+ y + z = 8 and xy + yz + zx = 20 , find the value of
i) x^3+ y^3+z^3
-3xyz
ii) x^2 + y^2 + z^2

Answer 1

Solution :

Given x + y + z = 8 ----( 1 )

xy + yz + zx = 20 ---( 2 )

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

= 8² - 2 × 20

= 64 - 40

= 24 ---( 3 )

i ) x³ + y³ + z³ - 3xyz

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

= ( x + y + z )[ x² + y² + z² -( xy + yz + zx ) ]

= 8 × [ 24 - 20 ]

= 8 × 4

= 32

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