if a+b+c=14,a2+b2+c2=74 and a3+b3+c3=434,then find the value of abc
Answers
Answered by
3
We know, (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) => (14)2 = 74 + 2(ab + bc + ca) => ab + bc + ca = 122 / 2 = 61
Again, using a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)
434 - 3abc = 14 (74 - 61)
434 - 3abc = 14 (13)
434 - 3abc = 182
3abc = 434 - 182 = 252
Abc = 252/3 = 84 (Answer)
Answered by
7
Answer:
84 is the answer.
Step-by-step explanation:
We know, (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) => (14)2 = 74 + 2(ab + bc + ca) => ab + bc + ca = 122 / 2 = 61
Again, using a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)
434 - 3abc = 14 (74 - 61)
434 - 3abc = 14 (13)
434 - 3abc = 182
3abc = 434 - 182 = 252
Abc = 252/3 = 84 (Answer)
I hope it is useful for you.
please make me brainliest.
Thanks
Similar questions