Question

if a + b + C is equal to 4 and a b + BC + CA is equal to 6 find the value of a cube plus b cube plus c cube - 3abc​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

- 8

Step-by-step explanation:

a + b + c = 4 and a b + bc + ca = 6

(a + b +c)² = a² + b² + c² + 2 ( a b + bc + ca )

a² + b² + c² = 4

(a + b +c)³ = a³ + b³ + c³ + 3( a²b + ab² + b²c + bc² + c²a + ca² ) + 6abc

(a + b +c)³ = a³ + b³ + c³ + 3{ab (a+ b) + bc ( b + c) + ca(c + a )} + 6abc

(a + b +c)³ = a³ + b³ + c³ + 3{ab (4-c) + bc ( 4-a) + ca(4-b )} + 6abc

(a + b +c)³ = a³ + b³ + c³ + 12( a b + bc + ca ) - 9abc  + 6abc

(a + b +c)³ = a³ + b³ + c³ + 12( a b + bc + ca ) - 3abc  

 a³ + b³ + c³ - 3abc = (a + b +c)³ - 12( a b + bc + ca )

 a³ + b³ + c³ - 3abc = (4)³ - 12( 6 )

a³ + b³ + c³ - 3abc = - 8