Question

if a + b + C is equal to zero then the value of (a+b)(b+c)(c+a)/abc is

Answer 1

a+b+c=0
a+b= -c
b+c= -a
c+a= -b
then -c*-a*-b/abc
-abc/abc
-1.
Thanks and keep going

Answer 2

Heya!!

Here is ur solution:-
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Given,
a+b+c=0
To find:
$\frac{(a + b)(b + c)(c + a)}{abc}$
Solution:-
$\frac{(a + b)(b + c)(c + a)}{abc} \\ = \frac{(a + b + c)(ab + bc + ca) - abc}{abc} \\ = \frac{0 \times (ab + bc + ca) - abc}{abc} \\ = \frac{ - abc}{abc} \\ = - 1$
Here we used a formula:-
(a+b+c)(ab+bc+ca)-abc=(a+b)(b+c)(c+a).

Hope it helped you.

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