Question

if 1/a+1/b+1/c=1/a+b+c where (a+b+c) is not equal to zero. what is the value of (a+b) (b+c) (c+a)​

Answer 1

Answer:

Answer is 0

Step-by-step explanation:

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

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

=> (b+a)/ab = (c - (a+b+c)) / c(a+b+c)

Cross multiplying (Since, a,b,c !=0 and a+b+c != 0)

=> c(a+b+c)(b+a) = - ab(a+b)

=> (a+b)( ca +cb +cc + ab ) = 0

=> (a+b)( ca + cc + cb + ab) = 0

=> (a+b)(b+c)(c+a)=0