if a+b+c=9 and a2+b2+c2=35 find the value of a3+b3+c3=3abc
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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
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