Question

if( 1-2a/a) + (1-2b/b) +(1-2c/c) =5 the value of (1/a+1/b+1/c) ^2​

Answer 1

Answer:

a+b+c=0 , a = -(b+c) , b =-(c+a) , c = -(a+b) .

2a^+b.c= 2.{-(b+c)}^2+b.c = 2b^2+4b.c+2c^2+b.c

=2b(b+2c) +c(2c+b) =(b+2c) (2b+c)

=(b+c+c) (b+b+c) , On putting b+c= -a

=(c-a) (b-a)

Similarly 2b^2+ac =(a-b) (c-b) and

2c^2+a.b =(a-c) (b-c) .

Now 1/(2a^2+b.c) +1/(2b^2+c.a) +1/( 2c^2+ab)=?

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

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

=-[(b-c)+(c-a)+(a-b)]/(a-b)(b-c)(c-a)

= -[b-c+c-a+a-b]/(a-b)(b-c)(c-a).

= - [ 0]/(a-b)(b-c)(c-a).

= 0 , Answer