Question

if a+b+c=6 and ab+bc+ac=11 find the value of a^3+b^3+c^3-3abc

Answer 1

$<b><i>Hi !$

Here is your answer !!

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GIVEN THAT :

a + b + c = 6

ab + bc + ac = 11

We Know ,

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

Putting the values , We get

=> ( 6 )² = a² + b² + c² + 2 ( 11 )

=> 36 = a² + b² + c² + 22

=> a² + b² + c² = 36 - 22 = 14

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a³ + b³ + c³ - 3abc =

=> ( a + b + c ) ( a² + b² + c² - ab - bc - ca )

Putting the values , We get

=> ( 6 ) { 14 - ( 11 )

=> ( 16 ) ( 14 - 11 )

=> 16 × 3

=> 48 ANS

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Thanks !!!