if a+b+c=10 and a2+b2+c2=38 a3+b3+c3=160 find abc
Answers
Given : a+b+c=10 , a² + b² + c² = 38 & a³ + b³ + c³ = 160
To find : abc
Solution:
a+b+c=10
Squaring both sides
=> (a + b + c)² = 10²
=> a² + b² + c² + 2(ab + bc + ca) = 100
=> 38 + 2(ab + bc + ca) = 100
=> 2(ab + bc + ca) = 62
=> ab + bc + ca = 31
a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)
=>160 - 3abc = (10) ( 38 - 31)
=> 3abc = 160 - 70
=> 3abc = 90
=> abc = 30
abc = 30
Additional info
one set of a b c are 2 , 3 & 5
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