Question

If a+b+c=0,1/a+1/b+1/c=0,find the value of a²+b²+c²​

Answer 1

Answer:

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Step-by-step explanation:

GIVEN THAT a+b+c =0 -------1²

now, 1/a²+b²+c² + 1/b²+c²-a²  + 1/c²+a²-b²

=1/a²+(b+c)(b-c)  + 1/b²+(c+a)(c-a) + 1/c²+(c+b)(a-b)

=1/a²+(-a)(b-c) + 1/b²+ (-b)(c-a) + 1/c²+ (-c)(a-b)    (from 1)

=1/a(a-b+c) + 1/b(a+b-c) = 1/c(c-a+b)

=1/a(a+c-b) + 1/b(a+b-c) + 1/c(b+c-a)

=1/a(-b-b) + 1/b(-c-c) + 1/ c (-a-a)                             (frpom 1)

=1/-2ab + 1/-2bc + 1/-2ac  

= 1/-2 (1/ab + 1/bc+ 1/ac )

= -1/2 (a+b+c/abc)

=-1/2 (0)  (from 1)

= 0