Question

5. If a + b + c =9 and 0% + b3 + 2 = 35, find the value of a + b3 + c3 - 3abc​

Answer 1

Explanation:

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Answer 2

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Given : a+b+c=9 and a2+b2+c2=35

To find : value of a3+b3+c3-3abc

Solution:

a+b+c=9  

Squaring  both sides

=> a² + b² + c² + 2(ab + bc + ca) = 81

=> 35 + 2(ab + bc + ca) = 81

=> 2(ab + bc + ca) = 46

=> ab + bc + ca = 23

a³ + b³ + c³ - 3abc  = (a + b + c) (a² + b² + c²  - ab - bc - ca)

=>  a³ + b³ + c³ - 3abc  = 9 ( 35 - 23)

=> a³ + b³ + c³ - 3abc  = 9 (12)

=> a³ + b³ + c³ - 3abc  = 108

a³ + b³ + c³ - 3abc  = 108